Sometimes you screw up and feelings are hurt and it’s unquestionably your fault. If that’s the case, you should apologize. It’s the right thing to do.
The trouble with apologies though, is they very easily turn into displays of weakness / fear / low value / submission. Then instead of repairing the damage, they actually do further damage as you entitle them to enrage against you even more than before. People always feel better at ease venting anger toward someone in lower status than them, than venting toward someone higher status than them. Thus a groveling apology creates greater social distance between you.
In case you didn’t hear that correctly… I’m saying you’re probably better off not apologizing and letting them be mad at you, than going down on one knee and begging forgiveness. You don’t drop your status and beg.
All you should do is acknowledge you did the wrong thing and if something is possible to be done to correct a situation you have caused, state a plan of correction and follow through on it. You don’t “act sorry” though. To apologize like a boss, just acknowledge and correct.
Then once the apology has been stated, you don’t go back and rehash it endlessly. You’ve apologized, it’s up to them to figure out their emotional state after that. If they keep coming back for another helping of angst and drama, state you’ve already apologized and refuse to be drawn into further debate.
Gifting is also a potential tool to use as well, but you use gifting to simply frame the acknowledgment of your wrongdoing more seriously, rather than attempt to buy their love and positive attention back. Trying to buy their positive attention back is also a display of low value. The purpose of something like flowers is to force them to pay attention to the apology. You’re making them acknowledge your acknowledgment.
The other trouble with gifting is that it can turn into a behavioral reward for them to be all dramatic and hurt at you. It only takes a couple of times trying to buy your way out of the dog house and it would be completely rational for them to start trying to figure out ways to get you into the dog house. A couple rounds of that and you’re a big Beta pinata full of cash and goodies.
Anyway… I love The Big Bang Theory… watch both videos.