Dual Wielding feat something is backwards

Enhanced Dual Wielding. When you take the Attack action on your turn and attack with a weapon that has the Light property, you can make one extra attack as a Bonus Action later on the same turn with a different weapon, which must be a Melee weapon that lacks the Two-Handed property. You don't add your ability modifier to the extra attack's damage unless that modifier is negative.

So i can dual wield with two light weapons, but if I want to duel wield with a rapier and a dagger, I have to take the Dual Wielding feat that is copied above.

For this to work, I have to attack with a weapon that has the light feature, the dagger, then attack with the rapier.  A dagger is about twelve inches long, let's say.  A rapier is about fifty inches long.  So I attack with the dagger and am close in with my enemy, then create distance between me and my enemy to attack with the rapier.  Okay, that does not make sense.

 It only makes sense for a longer weapon to set up a shorter weapon.  The use of the longer weapon creates an opening that can be taken advantage of with the shorter weapon.  I step in and stab with my dagger  A dagger does not create an opening for the rapier.  I stab with my dagger, then as soon as I step back so I can use my rapier, my enemy has the opportunity to form some kind of defense.  

I realize there is a lot of suspension of disbelief in this game, but this just bothers me.  I also searched to see if anyone else made this observation but did not find it.

And why is a rapier (2 lbs), which is lighter than the scimitar, (3 lbs) not a light weapon when the scimitar, which is heavier than a rapier, is a light weapon?

I would love to roll up a rogue (swashbuckler) dual welder using a rapier and dagger.

thanks

This is one of those times where you either need to grit your teeth and bear it or just learn to live without if the mechanics really are that difficult for you to run with. Weapon stats have a very limited relationship with reality, so trying to pick at which got what keyword is a non-starter. At the end of the day, you can indeed dual wield a rapier and a dagger for one feat. For Rogues in particular, the order doesn't matter a ton since the point of dual wielding for them is mostly just giving yourself a second chance to proc Sneak Attack if the first roll missed.

Or if that's really too much, just use a shortsword instead and pretend it's a rapier- the difference is a single point of damage on average for the weapon itself, and not getting to add your DEX mod to the dagger attack in exchange for saving yourself a feat.

yeah, if you wanna talk about "dagger", "rapier" and "scimitar" as DND weapons, you just have to accept that they are different titles for

dagger=1d4

scimitar=1d6

rapier=1d8

the listed weigh doesnt affect anything but possible encumberment.  And they all have the same reach, which, ugh, fine.

Also, if you think the rules are a bit wonky for having to attack with a dagger first, then scimitar, wait till you meet Rosie the Riveter.

 https://www.dndbeyond.com/forums/dungeons-dragons-discussion/rules-game-mechanics/241063-rosie-the-riveter

Dual Wielder is a really bad feat unless you use it with 2 Light weapons, and one of them has Nick. Then you can use the Nick property to make your "off-hand" attack, leaving your bonus action free to make the extra attack of Dual Wielder with your "main" weapon afterwards (quotes because there isn't really a concept of "off-hand" weapon in 5.5e). This is great for a gish to trigger damage rider spells like Hunter's Mark or CME, but the feat alone just doesn't compare to simply use the Two-Weapon Fighting style, which does add your ability modifier to the damage.
The fact that this is the only scenario in which Dual Wielder is actually beneficial leads me to believe that it was intended to be combined with Nick by design. Nick frees your BA, so now you can use it for Dual Wielder.