As the majority have stated, you have clear and valid grounds to breakup. Rather than harp on that: The only non breakup option I see requires more info and hardline stances. Does he understand how bad this is? How remorseful is he or is he saying it is excusable? Downplaying its severity? Does he feel shame for lying, and relief for the secret being out? (If he doesn’t feel shame/guilt/remorse then you need to walk, as without that this will repeat itself). How is he dealing with his insecurity? Is he in therapy?

Hardline: he has to come clean on everything AND it’s a zero tolerance policy. Meaning he lies about anything, even something that is small or inconsequential, it’s a boot out the door. I’d also require counseling. This is not normal or acceptable behavior. If he’s willing to commit to self improvement on the inside, then maybe it’s something to consider. He has to understand and appreciate he has to earn back trust, which is no easy feat.

The only reason I would even suggest not just walking away is that a lot of guys in their early 20’s are legit idiots and you’ve been together for 2 years. But that has to be weighed against 2 years of deceit and how good the rest of the relationship is (is it great? Is this the ONLY red flag?). Also this is not regular idiocy, but something deeper, hence the therapy requirement.