SoAsh...in my first marriage, I was a wayward wife, with a somewhat similar sitch to yours (as in, how could I have cheated like that? What was I thinking?) Remorse, regret, etc.
My sitch was a bit different in that my ex-h didn't just find out everything all at once and leave like yours. But there are enough similarities that I would like to offer you my perspective.
Here is the thing: no matter how you keep searching for some "reason" outside of yourself for why you did this, you are not going to find one. Therefore, you cannot really offer your husband any "reason" for what you did. And further...that means all you can give him for a "reason" is the truth: "I did it because I wanted to and I felt entitled."
Now that you've been caught, you want to back-peddle and take it all back...but that is pointless. That will not help you ever figure out why you felt entitled, and why you would hurt the person you were supposed to love and protect.
After my first marriage ended, I did all I could to understand affairs and why they happen, and what I found out was this: If you were the cheater, the problem was ALWAYS within YOU.
So...now that your husband has discovered the truth of what you have done, he has also seen the ugly truth of what you will "do".
You cannot change this truth. You cannot apologize, what is the point? You cannot find some other reason for it. The reason lies within you, and you must face that you did this horrible thing, and further face that your husband has every right to withdraw his love from you now.
Once you accept that, and focus inward, there may be a chance to rebuild things with your husband. But being focused on YOUR pain and how much you miss him and want him back, it NOT going to help you. You need to focus instead on this: What is it within ME that made me behave in a cruel way to the man who loved me?
Find the answer to this. None of us know the answer, as it is different for all cheaters. But here is a hint: it is not because you didn't get enough sex from your husband, and it is not because of your childhood. These were adult decisions you made, and now you must use adult reasoning to find out "who" you really are.
I feel for you. I was in your shoes at one time. We are divorced now, and my ex-h hates me. I can't take back what I did.
But...I did find out who I am, and worked to change it, so that I could be proud of myself in the future.