Scenario 1: So let's say you and your spouse are in a heated argument and you say something that really pisses her off and she hauls off and slaps you in the face. When you tell her that hurts, she says "Sorry. But you really pissed me off."
Scenario 2: Let's say you and your spouse are in a really heated argument and you say something that really pisses her off and she hauls off and slaps you in the face. When you tell her that hurts, she says "I'm so sorry. You didn't deserve that." And then a few days later she comes to you and says "I wanted to apologize again for slapping you. I don't know what got into me and you didn't deserve that treatment from me. I have found an anger management program and am starting those classes later this week."
Scenario number one is admitting it. She acknowledges that she slapped you. Does that help you? Does that make you feel respected and seen?
Scenario number two is owning it. She acknowledges that she slapped you, she acknowledges that you did not deserve it, and she has taken steps to rectify the situation and do better in the future (this also shows that she knows this is a HER problem and not a you one). Does that help you and make you feel respected?
Admittedly this is kind of an extreme scenario, but I can tell you as a former BW my WS admitting he cheated really didn't do much for me because that admission was not followed up by any action whatsoever; he was just saying the first 'sorry'. What would have helped me is him apologizing, then figuring out what steps he could take to be a safer partner in the future and doing them on his own without expecting me to make appointments or send links or whatever. You are taking a good first step posting here.
So how can YOU own it?
Just a few thoughts/suggestions from a BW.
Therapy. Then some therapy. Then some more therapy. Find a therapist that can help you to unpack why you made the choice to cheat instead of a healthier one.
Be unfailingly honest. I can imagine this one is really hard in the earlier days when you're trying to break old patterns, but you MUST be honest. With your BW, with your therapist, and most of all with YOURSELF. Even if the question is hard, even if the answer is one that may lead to a bad outcome for you (especially so in that case IMHO), even if anything, NO. MORE. LYING.
Be transparent. How would you feel about your wife going through your phone/computer/texts/sm messages right at this minute? If the answer is anything other than "absolutely fine" then you still have some work to do here. Also, once you get honesty and transparency in line... it's just such a better way to be authentic and in your space - when you don't have to put mental effort into hiding things life is so much simpler and more peaceful (that's my 0.02 anyways).
Be accountable for your actions and thoughts. It's really easy when apologizing o add a but. I'm sorry.... but I was mad. I'm sorry.... but I felt like you didn't love me. I'm sorry.... but you hurt me too. Accountability means removing the but. I'm sorry that my actions hurt you so much. I'm sorry that I didn't make a different choice. I'm sorry that I damaged your ability to trust me.
Collect knowledge like pokemons. Knowledge is power. You're posting here which is a good way to get that. But also, read everything you can get your hands on about infidelity and how it affects the betrayed. Read every book/article/podcast/etc suggested to you here by other waywards. The more you KNOW, hopefully the better you will begin to reach UNDERSTANDING - both of what your wife is going through and also how you made the choice to do this.
Talk talk talk. Don't wait for your wife to bring up the A. It really would have helped me for my xwh to ask me questions about how I was feeling/doing, to volunteer time and effort to openly discuss it, and by so doing, showing me that I could freely discuss my infidelity-related thoughts and feelings and struggles with him.
Fall into a shame spiral. Yes, cheating is shameful and feeling that and processing it is vital to your healing and growing. But feel it, let it pass through, and then move forward. You are greater than the sum of the worst thing you've done and you deserve to live an emotionally healthy existence.
Get defensive or shut down. I imagine this one is very difficult but you cannot get defensive when/if your BW talks about the A. Defensiveness shuts down your ability to truly empathize with and hear her, and if you want R you need to be able to do both of those things. Also do not ever, ever, EVER ask her when she will get over it. There is no short cut to "getting over it" for a BS.
Omit truth to 'protect' your spouse. Even if you know that sharing a truth will hurt them, you have to say it. I can tell you from my experience that what ultimately killed my marriage wasn't the A, it was all the lies and half-truths after it. I knew my xwh well and could totally tell he was lying right to my face - and on top of the disrespect of the A to begin with, the lying was like salt and lime juice and acetone in that wound. I can say for me that I would much rather him have just told me the truth, even though that truth was hurtful, than to lie to me more in a misguided attempt at protection.
Make promises you can't keep. My xwh was all about the "I promise" after dday. I think he thought he really meant them, but he didn't have the fortitude to see anything through. The best you can do is promise to try and do the work and put in the effort to show that you're keeping it.
Take on others feelings. This one is tricky, but IMHO part of the really hard work for a WS (and a BS too) is learning how to set and hold healthy boundaries. Yes, your actions caused your wife immense hurt - YOU take accountability for YOUR actions. You can apologize to her that they caused her hurt. But ultimately SHE has to own HER feelings and figure out her new reality - you can help with that process for her by being transparent and honest, by allowing her freedom to discuss her feelings with you etc, but you can't do that work for her. You'll read it a lot on here about how each partner heals themselves and then they both heal the M.
Give up. Yes marriages can and do survive infidelity, but the ones that do have WS's who are willing to climb any mountain, dig into any hole, and shine a bright light on all of their stuff. It is not for the faint-hearted. It's okay to have doubts and fears, but have them while still doing the tough stuff anyways. Your willingness to face down your fear and shame and do the work will speak volumes to your wife, believe me.