I just started the game and I went and got a third pixpet egg and cannot place it because of my house size (I'm assuming). Since it's not hatching I guess it's inactive? What is the point of keeping more pixpets than your house can have active? And is there a way to sell an egg after you've claimed it from a hoard? Or am I stuck with it?

Thank you in advance!

Gotcha and very cool! Is there a good reason to have more pixpets? Rather than focus on just 2 for instance?

It really depends on your playstyle and what your "goal" in the game is to be honest.

Some pros for having multiple pixpets of different colors is that they can find a bigger variety of eggs for example. The more hoards you send one pet on, the higher it's level gets and the longer the hoard and cooldown timer get, so having multiple lower tier pets for quicker hoards may be something to consider although higher tier pets tend to bring more PC and rarer items.
Another factor is simply; people like collecting things and filling up their pixdex but some people may prefer to stick to a few, well 'trained' pets.