Questions: Dating

So, recently talking to my bestie, she and I realized how both our boyfriends tend to lack empathy.

My boyfriend is so stubborn that he isn't wiling to yield on certain things, or, even consider that he could be in the wrong. It has resulted in fights between us, ending with him being confused. I ask him questions like "if you were in my shoes, and I said that to you, how would that make you feel?"... and he then will come to realization, and apologize, or at least meet me halfway.

Do you think its possible to make someone more empathetic?

I've met this guy 2 months ago at an extracurricular activity and immediately thought he was cute and I had the vibe that he liked me too, he even asked for my ig. Around 2 days after that, I couldn't stop thinking about him so I sent the scary first text and that's when we started texting constantly, he asked me "out" but didn't say it was a date explicitly, we had a lot of fun and saw each other 2 days after that, and so on. He initiates physical touch like back patting or holding my hand for a second etc, he gives me flowers, we talk about deep stuff sometimes until dawn, and overall I'm completely sure we like each back. However, even though he always has fun on our dates, I have to initiate them almost all the time. It's like he avoids telling me the exact day he will be free so I always have to suggest it. I'm feeling really uncertain about this whole situation and want to let him know how I feel because I'm a 100% sure he feels the same way but he's either scared of rejection, or scared of getting hurt in a future relationship. What do you think I should do?