Can you push someone to break up with you?

i think I pushed my (ex) boyfriend into breaking up with me yesterday.

he was leaving for a funeral he had to go to in south africa, and said he was unsure of when he would be back. the night before I had told him that I was unhappy because he works a lot (he owns a company) and I understood that, but at the same time I felt like he wasn't giving me the attention that a girlfriend deserves.

we had been together for over 3 months and he has only taken me on two 'real' dates, where it's just us. the rest of the time was just hanging out at his house or going out with his friends where he would invite me to something he already had planned with them. I complained about this, letting him know that all it takes is a simple text saying 'i miss you' during the day or a call at night to say 'i miss you' and maybe a date here or there and that I've never expected anything fancy.

yesterday he met me at a starbucks before leaving for south africa. he seemed really stressed (this all happened last minute, the death wasn't expected) and he kept insisting that I was unhappy. I told him of course I was unhappy that he would be gone and wasn't he unhappy that he would be gone from me too?

basically things snowballed out of control and he ended up saying that during the talk I made him see that work is becoming more of a priority for him and that its unfair to me to 'play second fiddle' to that. I told him that if he wanted to break up with me not to blame work and just say he didn't want to be with me. he said he didn't want to break up but he felt it was the 'right' thing to do.

we just kind of walked away from each other without a goodbye and me saying I cared about him.

i deleted him off of fb and took us out of a relationship immediately. I was crying so hard. I ended up writing him an email saying that we were both really stressed, and that things got out of control and that I hoped we could work through it because I care about him and he does make me happy and that he has my number.

he has yet to respond to the email or call/text, and I don't really see why he would being that I deleted him from fb.

i don't want to be 'that girl' who begs but I truly feel like I pushed him so hard because we were meeting just to say goodbye until I felt like he was going to break up with me and brought it up and he said that wasn't the case at all...but then somehow it ended up like that.

now I'm embarassed of the email I sent him. what do I do?