They're young.bonding It's like marriage but with permanent side effects, so rushing into one would be bad worst case fatal in some stories. Also I'm not sure if there was a time skip or not but if they are old enough the best answers I can give us that
1) he is that bonding would take away his heats but leave an obvious mark.
2)His family is overbearing, and if he bonded he would be cut off financially. He needs the money to get an alphas education and job opportunities.
But asking his uncle to help him leave the family will give him the chance to fully commit.
3) being publicly known as an alpha means he would get in trouble if caught. He's applying for alpha jobs and is living a secret life, if found out he could be arrested. His family will fall apart since they are involved too. All those elite connections gone.
I also don't quite get why the first couple doesn't bond since they have decided to be a pair...is it something to do with whatever drugs they used on him to fake his alpha?