Well... I'll try to give feedback then. And good for you for working with your therapist! That is commendable.
You are not responsible for your partner's happiness/unhappiness or any other emotion they may be experiencing.
I get it on some levels, but I'm not sure how to bring that into my treatment of my partner(s). I mean, asinine behavior is hurtful and if I chose to go there, then I go there knowing that I'm probably going to hurt someone, so doesn't that leave me with some responsibility for their emotional state?
You are not responsible for WHAT they feel. They feel whatever it is.
Is "I am responsible for taking care of my own health and well being, and for that of my partner" in your implied or stated covenant/agreement/standard of relationship? Do you give them the right to have "support/nurture" behavior from you?
If so, then you are responsible for your partner's HEALTH and WELL BEING. Your behavior contributes to that because your behavior helps create the environment for your shared relationship. Your behavior toward your partner includes support/nurture behavior from you should they need comforting. You are not responsible for WHAT they feel, but you are responsible for HOW you tend to them, when they feel whatever it is. Happy joys, or sad concerns that they might have -- hopefully you tend to them with loving kind behavior and not asinine behavior.
If you are the one being asinine? That is your BEHAVIOR. Not your feelings. If the person receiving this behavior is your partner, they probably hope that you choose to apply loving and kind behavior toward them rather than choosing asinine behavior toward them. They do not wish to be hurt by you, their partner.
If you do not make it a habit of choosing loving and kind behavior toward them, and choose asinine behavior to treat them with, they may feel yucky. In time, they may tire of feeling yucky and choosing "put up with it" type behavior. They might choose new behavior: ask you "Are you aware of what you are doing? And that is it asinine?" You risk being asked that in choosing asinine behavior toward partner.
Having learned behavior X is asinine, if you CONTINUE to apply that behavior? They may choose a new behavior for themselves so they can feel better and yucky free: Choose to break up with you. You risk that also.
If your relationship agreements
with your partner include the responsibility of "I am responsible for tending my own and my partner's healths: mental health, emotional health, physical health, and spiritual health" then you are in violation of that agreement/trust. They have every right to dump you then for not honoring agreement.
So... basically what behavior you do is still up to you. You are always free to choose your conduct. But you are not free from consequences of your choice, and you are not free from the obligations, agreements and responsibilities you signed up to honor and tend when you signed up to be in relationship with your partner.
Where is the confusion?
Is it that your partner is trying to make you responsible for how they feel? If your assess and find that your conduct toward them is appropriate, loving and kind -- then could it be that they may be avoiding personal responsibility?
Everyone has to hold their own baggage.
You can't MAKE your partner feel happy, or feel sad or feel whatever. But you CAN acknowledge that your behavior affects your partner in some fashion because you are in relationship. And choosing healthy, loving, kind behavior to treat them with ups the odds of them feeling appreciated and cared about by you. You can't MAKE them feel loved (maybe they suffer depression and that clouds their perception internally) but it ups the odds for them to be able to feel that because you help create the loving EXTERNAL environment in the relationship for them to feel it IN. (Whatever they have going on in their internal environment inside their own heads... that's not in your control. Things like depression could need a doctor's care.)
To be in right relationship with you partner, you honor the agreements you have made between you.