If you had an affair, online or off, with someone, you know. If said person told you, “Look, my SO isn’t okay with this” and the two of you continued with sexual involvement, it counts as an affair. You cheated.
So how the hell could you claim that you didn’t know it bothered that person’s SO when she found out? That is one of the lamest excuses I have ever encountered for anything. The level of “it’s not my fault!” bullshit involved there is astonishing.
When you fuck up, apologize. It’s a vital part of getting your shit together. When you apologize, you’re acknowledging that what you did was wrong and that you are sorry that you did it. You’re saying that you will make a serious effort not to do it again.
If you just feel a “sorry I got caught” then don’t bother apologizing. You’d just be telling more lies.
If you’re over the age of 4 and you have to be asked for an apology, it’s insincere.
If you can’t be bothered to apologize, you aren’t taking responsibility for your actions.