You can't "make" anyone (see) you "love them".
Each person has their own idea of what love is supposed to look and feel like. Everyone has their own litmus test:
"If you loved me you would...etc or You wouldn't have...etc"
Unless you know what (their) expectations or needs are then it's impossible to give them what they want.
You may simply not be the "right person" for them!
On the other hand if you hurt someone it's important to remember "forgiveness" is not done according to (your) timeframe.
You don't get to tell them to wipe the slate clean or become frustrated with them because you are the one that hurt them. The ball is in (their) court. Trust doesn't happen instantly or easily after hurting.
All you can do is sincerely apologize, offer an explanation of why you did what you did along with what you've learned and why it will never happen. Afterwards let the person know you don't expect things to immediately go back to the way that they were but you're prepared to do (whatever) it takes to (earn a second chance) to become the kind of person they thought you were.
You end it by telling them you're going to give them some time and space to decide whether or not they want to salvage the relationship.
In the meantime you work on yourself and hope for the best but prepared for the worst. Ideally with each failed relationship we learn more about ourselves and what (not) to do in our future relationship including selecting the right partner.
You must be honest with yourself!
If you were truly "in love" with your mate would you deliberately do anything that would cause them pain? Figure out how you justified in your mind that is was okay to do what you did?
The first lie we tell is to ourselves. It's the lie of justification.
Why do you (really) want to come back? Remember he/she is going to be the same person they were when you felt it was okay to do what you did.
Sometimes you're better off leaving a broken mirror on the ground rather than risk cutting yourself up trying to put it back together again.