One of the drawbacks of the hand crossbow (and crossbows in general) is the Loading property. Under most circumstances, the character needs one hand to hold the weapon and another to handle the ammunition. This normally precludes the idea of handling anything else including weapons, shields, or potions. Based on the description of the Thri-Kreen's secondary arms, they can be used for both the handling and the reloading of a Hand Crossbow while using the primary arms for other things.

"You have two slightly smaller secondary arms below your primary pair of arms. The secondary arms can manipulate an object, open or close a door or container, pick up or set down a Tiny object, or wield a weapon that has the light property."

Am I wrong or does this not make the Thri-Kreen the best race for using a Hand Crossbow?

I'd argue that if you can wield a light weapon, loading a crossbow should be no problem.

I'd even suggest that you can wield a two-handed or versatile weapon with your primary hands, and then when not swinging that around you can use one of those hands to load--freeing up your remaining secondary hand to wield a light melee weapon.  Take the Dual Wielder feat, and this would give you the option to dual-wield with a two-handed or versatile weapon, with your bonus action attack being either melee or ranged, without having to swap out weapons.  Even without the feat, you could choose between attacking with the two-handed weapon or dual-wielding your light melee weapon and your hand crossbow.  Heck, you could even dual-wield hand crossbows, I reckon.

The Basic Rules do say that two-weapon fighting is done with melee weapon attacks, but given hand crossbows have the light property, I'd say it's intended to work.

Edit: Nah, I was wrong. I have nothing to add here.

It's the best at using any light weapon since it has 4 arms to do so, it can wield up to 4 club, dagger, handaxe, light hammer, sickle, scimitar, shortsword, or 3 if wielding a hand crossbow, since it requires a free hand to reload.

But wielding that many weapons doesn't let you attack any more with them than your action allow you though.

You could try shield+hand crossbow+scimitar or something like that.

You can do a hand crossbow, a shield, have a hand free for reloading, and hold either a rapier or Spellcasting focus in your other, other, other hand all at the same time. Been saying it since the UA came out.

So this race is basically General Grievus? But even wielding four swords doesn't give you more attacks than two do, sadly.

This gets more interesting for casters who can now hold their spellcasting focus as well as weapons/shields, for Valor/Swords Bard or Hexblade Warlock or Bladesinging Wizards. Similarly, you can now wield two light weapons for dual wielding AND a shield. Very powerful at low levels, and tbh, probably at high levels too.

Another intersting option is the Wild Magic Barbarian. It's up to chance, true, but you can now dual-wield heavy weapons, if you take the Dual Wielder feat, or one heavy weapon and one light weapon. The reasoning is that "Heavy" requires two hands, but doesn't prevent dual-wielding. Usually, all Heavy weapons required two hands, so it didn't matter. Now that you have four, though... this race should have been made Small, and it's the first time the Heavy feature would make mechanical sense.

At level 6 you should be a Battle Master Fighter taking the quick toss maneuver, cross bow expert, and sharpshooter. Wield shield and net in primary hands hand xbow in secondary if you want more AC. Use quick toss to throw a net as a bonus action. If your net hits action surge and sharpshooter for lots of attacks with advantage and lots of damage. 

Quote from Darkaiser >>

One of the drawbacks of the hand crossbow (and crossbows in general) is the Loading property. Under most circumstances, the character needs one hand to hold the weapon and another to handle the ammunition. This normally precludes the idea of handling anything else including weapons, shields, or potions. Based on the description of the Thri-Kreen's secondary arms, they can be used for both the handling and the reloading of a Hand Crossbow while using the primary arms for other things.

"You have two slightly smaller secondary arms below your primary pair of arms. The secondary arms can manipulate an object, open or close a door or container, pick up or set down a Tiny object, or wield a weapon that has the light property."

Am I wrong or does this not make the Thri-Kreen the best race for using a Hand Crossbow?

 They're the best for Crossbow Expert, yes, because they can dual wield a Heavy Crossbow and a Hand Crossbow.  They can also combine a Hand Crossbow with a Shield (and Rapier/Whip) without needing an Artificer on tap.