ok, then I'll assume we're still on the same page, because #16 was a point I agree is correct.

Quote from Plaguescarred>>

There is no rules explicitly backing up what you claim.

Yes there are.  I provided them.  There are only two.  Do you want them again?

You can make an opportunity attack when a hostile creature that you can see moves out of your reach. To make the opportunity attack, you use your reaction to make one melee attack against the provoking creature. The attack occurs right before the creature leaves your reach.

Reach. This weapon adds 5 feet to your reach when you attack with it, as well as when determining your reach for opportunity attacks with it.

In absence of that and with Sage Advice also going againt your claim, its pretty clear that claim is wrong. 

The SAC confirming my claim:

How does a reach weapon work with opportunity attacks?

An opportunity attack is normally triggered when a creature you can see moves beyond your reach. If you want to make an opportunity attack with a reach weapon, such as a glaive or a halberd, you can do so when a creature leaves the reach you have with that weapon.

It doesn't say you can make an opportunity attack when a hostile creature that you can see moves out of one of your reaches.

You only have one reach, which for a PC is going to be 5 feet base, barring some other special rule.  A reach weapon will, under specific circumstances, modify that one reach to be a different value.  But you only have one reach at any given time, and that reach is still 5 feet while you are holding a reach weapon, which is why you can't use a whip to cast a touch range spell at 10 feet - because your reach is 5 feet, and the whip doesn't modify your reach while casting the spell. 

Just your reach. Taken that most creatures have a 5-foot reach and having a Reach weapon desn't give you an additional reach, but add 5 feet to your reach, it mean you now have a reach of 10 feet with a glaive.

This is exactly right.  You have a reach of 10 feet with a glaive (meaning an attack with a glaive, and nothing else).  You don't have a reach of 10 feet with your hand whole holding a glaive.

When welding it, anyone not moving past 10 feet doesn't trigger OA as they don't leave your reach.

Yes, they do.  Your reach is 5 feet, which the glaive does not modify, so when they leave from 5 feet away to 10, they leave your reach.

That is why SAC explicitly says if you’re wielding a halberd, a creature that is right next to you could move 5 feet away without triggering an opportunity attack.  

 The sentence you're quoting contradicts the sentence before it, which I provided above.  When the SAC contradicts itself, as with any rules contradiction, you have to choose which to follow.  So, take your pick:

1. The rules for OAs and the rules for Reach weapons and the SAC sentence before the one you quoted confirm I am right.  I have provided all three rules in this post.
2. The sentence you quoted is the only rules source anywhere making the claim it is making.
   1. Note that this change to the sentence would bring it in line with the other three rules I have given you:  For example, if you’re wielding a halberd, a creature that is right next to you could move 5 feet away without triggering an opportunity attack that can be made with the halberd. (I put the necessary house rule in italics).
   2. Meanwhile, enforcing the sentence you quoted would require changing at least one of the definition of Reach or the definition of Opportunity Attacks.  
      1. If you change Reach - which is the change you were just advocating for - you will let casters use whips to cast touch spells at 10 feet.

So, make your own decision, I guess.  But the rest of us will follow the post-errata PHB and the first half of that SAC ruling.

But you are leaving half of SAC that doesn't support your claim here's the problem. Why would WoTC says you don't provoke OA moving from 5 feet to 10 feet with an halberd if you really were?

EDIT Also the first part of SAC also doesn't support the claim that you can use a glaive  on an enemy moving from 5 to 10 feet like some are making since it doesn't leave the reach of that weapon.

Put aside the “complete the 5 foot OA with your whip” argument, and focus on ironing out “is there a 5 foot OA at all?” argument first. Quinn’s analysis is thoughtful and correct,  “your reach” is always 5 feet, with your Unarmed Strike even if nothing else. Leaving your 5 foot range ALWAYS provokes an OA.

What weapon can you use to complete it once it’s triggered? We can disagree on that, but let’s get the fundamentals straight first instead of jumping ahead. 

I found a twitter from Jeremy Crawford that could explain the discrepancy between rules and SAC  https://www.sageadvice.eu/if-a-monster-has-2-different-reaches-when-does-it-get-opportunity-attacks/

@JeremyECrawford The SA answer is only about making an opportunity attack with the reach weapon, not with another reach you might have.

Otherwise, the SAC and the rules are not sync well on that matter then. Let's re-examine with fresh eyes and JC's take rather than SAC alone; 

RAW:

You normally have a reach of 5 feet. 

You add 5 feet to your reach with a reach weapon to determine OA with it.

You can make OA when a hostile creature that you can see moves out of your reach. 

 SAC:

If you want to make an opportunity attack with a reach weapon, such as a glaive or a halberd, you can do so when a creature leaves the reach you have with that weapon. If you’re wielding a halberd, a creature that is right next to you could move 5 feet away without triggering an opportunity attack. (with the halberd #JC)

Conclusion:

So if a creature doesn't leave the reach you have with a weapon, you can't make Opportunity Attack with it. Therefore, you can only make Opportunity Attack with weapons that creature leaves the reach of. So moving beyond 5 feet provoke from weapons with 5 feet reach, moving beyond 10 feet provoke from weapons with 10 feet reach and so forth.

Looking at it this way, its seems more RAI than RAW to people that claim the Reach property; 

This weapon adds 5 feet to your reach when determining your reach for opportunity attacks with it. 

So when determining if a creature moves out of your reach, it should be 5 feet for most weapons and 5 more for reach weapons. How could you make an OA with a weapon that a creature didn't move beyond the reach of? Saying that once you provoke, you can attack with any weapon available seems to open up a can of worm to me. Going back to a sword and whip combattant, when an enemy moves beyond 5 feet, while he did indeed move out of your reach (with short sword, unarmed strike) he didn't not move out of your reach with a whip. SAC seems then pretty much clear you couldn't use it below it's respective reach to make the OA.  About JC tweet chain seem to support that as well;

@JeremyECrawford "Your reach" means whatever reach of yours is relevant at the moment. 

I’ll agree that that is RAI. But I don’t agree that OAs are written in a way that RAW precludes you using your whip (or whatever you’re wielding) to complete an 5-foot OA triggered by reference to your non-whip Reach. But RAI, I agree, it’s not what they were shooting for.

Glad we got through the other part though, that’s all that the original poster was actually looking for before this can of worms opened :p

War caster says you can still perform somatic  components while holding weapons / shield