It's always bothered me that spellcasting clases are so powerful compared to melee classes. I found the idea of an anti-mage in earlier editions, and it fits quite well with something I'd like to try. I don't find 5e has the option to play this, without being a spellcaster. This defeats the purpose of being an anti-mage. So, by chance while browsing other homebrew content, I thought that the Monk felt very flavourful in regards to anti-magic.

This is what a few hours of speculation lead me to. I'm worried it might be a bit verbose, but I do like it. I'd like a second opinion to get it a bit more grounded :P I've only homebrewed feats so far, so this feels like a bit of an undertaking. I tried to balance it by taking the few features I want it to have at the levels other classes get them, and use Way of the Four Elements as inspiration for spell costs.

Way of the Falling Needle

3rd - Whisper in the Void
If you can see a creature's mouth while it is speaking a language you understand, you can interpret their words by reading their lips.
If, where your character lives, a language exists that the Deaf use, you learn this language.

Spells you cast using Way of the Falling Needle have the following rules:
Your spells have only Somatic components, and are not treated as spells;
as such they cannot be interrupted by spells like Counterspell or dispelled by spells like Dispel Magic.
You must still follow and any rules of spellcasting (e.g. Concentration).
Your spellcasting modifier is Dexterity.
You can spend a number of Ki Points (up to your monk levels - 5, divided in half)
to increase the level of a spell slot used for Dispel Magic and Counterspell by 1 for each.

3rd - Sound of a Falling Needle
You have learned to turn your inner peace outward, releasing a deafening silence on your surroundings.
You can spend 2 Ki points to cast Silence as an action. It becomes a 5-foot-radius Sphere centered on you, moving with you.

While this effect is active on you, you can make an an Unarmed Attack roll targetting a creature; you can choose to deal no damage.
This attack can replace any Unarmed attacks made as part of the: Attack action, or as part of a bonus action, or as part of a reaction.
If you hit, the area leaves you and fills the target's square, moving with the it until the end of your next turn: it then returns to you.

6th - Disrupt the Weave
Spend 3 Ki points. Until the end of your turn or when an attack hits, you can attempt one of the following maneuvers:

Make an Unarmed Attack roll targetting a magic item contested by the target's Strength (Athletics) check or Dexterity (Acrobatics) check.
If the item provides a bonus to AC or to attack rolls an damage rolls, the target may add the bonus to their roll.
If the attacker wins the contest, the attack causes no damage or other ill effect, but the item's magic is suppressed for 1 minute.

Make an Unarmed Attack roll targetting a creature, object, or magical effect. Attacks against objects or magical effects automatically hit.
If you hit, cast Dispel Magic on the target as if using a 3rd level spell slot.

These attacks can replace any Unarmed attacks made as part of the: Attack action, or as part of a bonus action.

6th - Needle in the Wind
When you see a creature within 60 feet of you casting a spell,
you can use your reaction and 1 Ki Point to make 2 Ranged Unarmed Attacks before the spell is cast.
If either attack hits, you can spend 3 Ki Points. Cast Counterspell on the target as if using a 3rd level spell slot.

11th - Puncture the Weave
You can cast the Antimagic Field spell as an 8th-level spell once with this trait.
You regain the ability to cast it this way when you finish a long rest.
The area of the spell is reduced to a 5-foot cube.
The duration is reduced to 1 minute.

11th - Absorb Magic
While supressing the effect of a magic item granting a bonus to AC or attack and damage,
gain this bonus to AC and attack and damage while supressing the effect.

17th - Deny the Weave
Apply any of the following following features to Puncture the Weave when you activate it:
No longer reduce the area to a 5-foot cube
No longer reduce the duration to 1 minute.

I have always liked the idea of an "anti-mage" subclass, but never really thought of it being a monk subclass. That being said, I really like the flavor you went for. 

My first suggestion is that some of the language could use some polishing. Secondly, I think having access to Antimagic Field at 11th level (even in a weakend form) may be a bit too powerful. The 6th level ability (Needle in the Wind) doesnt make much sense to me as you have to make a "Ranged Unarmed Attack." I would simply say for that one that at 6th level you can spend 3 ki points to cast Counterspell with a range of 60ft. 

Finally, my main question is why is it important that spells cast using this subclass are not "treated as spells"?

Cool subclass, I always like to see a new, balanced, and creative monk subclass. But aside from that, I think that magic classes are a little more than just glass cannons, but a glass gun.

They have a lot more mechanisms I mean, as in if they don't have resources then they can't use spells. A rogue perhaps taking their wand, another magic user using antimagic, disabling their vocal components or somatic components. A lot of things can disrupt a spell caster, you just need to do it quickly and know how.

Just saying that a melee subclass is still able to be on par with the magic casters.

I feel kaboo has strong suggestions, the couterspell in particular was exactly what I was thinking after I read the ability.  Keep it simple, the extra attacks are not really necessary.  Think of it as something similar to deflect missiles in terms of use.  The antimagic is very potent too.  I would also ask, why Dex modifier for the spell effects?  Why would you not just go with Wisdom as that is already a primary stat for monks and fits much more with how magic works in the world.  using physical scores for spellcasting modifiers always strikes me as too much double dipping for my liking and does not jive with the concept of magic.  At least it does not to me personally.

As an addendum to the counterspell ability, maybe lower the initial cost to 2, and allow them to spend an additional 2 to redirect the spell back at the caster (maybe 3 for the redirect).

All these responses are great! Thank you for your input!

@Kaboom

The language does need some polishing. I'll take some more time to do this when i post an updated version of this, from your suggestions.

The attacks before counterspell are to enforce this idea of everything this character being partially physical. In some form, contact is made before each feature. This is also partially why I want the spells to not be spells, as per the mechanics. They are flavored to be physical and mystical actions interrupting spellcasting. Secondly, if the spellcaster can simply counterspell back, this class would lose some power to the classes it is made to counter.

I understand that the "lesser" antimagic field is powerful, and it is mainly at level 11 because that is the level monks get a feature. On the other hand, it is not a requirement to follow this, as with the Hexblade. What if i moved this feature to level 15? This way:

It appears on the level a spellcaster can choose the spell, and

it appears 2 levels before the full feature, so it feels like a growing power and mastery, and finally

A lot of campaigns end at level 15. This way this ability becomes a "lesser" capstone ability.

@Bobob

I like your thinking. Should I maybe find space for a feature to gain proficiency in Slight of Hand and use it as a bonus action? This wayt the character can steal for example the arcane focus as an option.

Also, I do not find the classes are balanced :P You can't do much against a wish, or time stop, or wall of force as a physical character.

@Hero0

I do like that idea of deflecting the spell. This can replace the lesser antimagic field. The only problem here, is that I try to have options the character can use against non-spellcasters, so he has something to do the rest of the time. E.g. using powers against magic items, or silencing enemies, or conditionally allies.

I want Dexterity to enforce this idea that the actions done are mostly physical. Originally I wrote out the spells (dispel magic and counterspell and silence) and changed the wording to fit the non-spellcasting and use Dex where I wanted.

Also, Wizards get to use their primary stat for their counter-spell and Dispel magic, while Monk's would get a secondary stat for it, making them more mad, and the idea here is to be at least as good at main spellcasters, but only at this one thing.

My argument against using Dex takes into account that monk features such as stunning strike already use wisdom as your saving throw modifier.  No reason to make people have multiple different saving throw modifiers to work with.  If stunning strike doesn't use dexterity, there is no reason these other abilities would need to either as Stunning Strike is also a physical/mystical ability.  Also follow the KISS rule.

I'll  change it to wisdom.