Because he broke your trust and you know you can't monitor him 24/7.
But, for me, that he would openly mention to you about finding other girls cute is more disturbing. This shows either a lack of awareness or concern for your feelings, indicating a lack of respect.
Whether you stay with him or not depends on whether he's able to regain your trust. If it's a newer relationship it may not be worth it to bother with him further. If it's an established relationship then it's more worth your time to give him a second chance.
If you do this you'll need to establish clear boundaries as to what exactly you find unacceptable. Everything from glances at other women to porn needs to be covered so he understands exactly what you require.
You'll also require giving him some basic trust until he's able to earn back your full trust.
I would imagine the shorter the relationship the higher chance of the relationship not working out in the long run. putting ultimatums on people early on is not a healthy start, but it's what's required
If you stay it's a risk. There's no way to remove the risk or to make it easier.