You are actually asking "how to argue like a woman".

Don't bother. Unless you are in a court where there is a judge and or jury, there is literally no way to win an argument. If you have points to make, then make them. Leave the other retard to babble about their own shit.

the trick is not argue with retards.

arguing is what they want. the moment you argue with them, they have won.

the only winning hand is not arguing with them.

Women argue by getting you emotional and by changing the subject.

Stick to facts. Ignore emotions. Don't allow them to change the subject the nanosecond you prove your case.

Best choice is not to waste your time and energy on that crap at all, and just demonstrate rather than explicate.

Edit:

Also, a great technique is called fogging. Read the book "When I Say No I Feel Guilty". It has this and other techniques. Fogging is when someone makes some emotionally-based accusation, and you say something along the lines of "I can see why you'd feel that way". This disarms them by acknowledging their feelings without admitting wrongdoing. Rian Stone goes into this on his YouTube channel frequently.

It's usually best to not argue your case in front of your boss. I would have said, maybe we should each discuss this in private with you (boss).

honestly in that situation, acting professional, not complaining in a heated argument and asking to have private discussion is going to win you points with a boss.

Ask your boss for a meeting in private to discuss. Tell the boss you didn't want to bring things up and agitate things.

Be professional, factual and to the point.

It can help to remember every petty detail

When people want to argue with me, most of the time i win cause I make them sound stupid. I never realized how I did it until I read your question. Here’s how I think I do it

I twist their words? When they say something wrong, use it to show how most of what they say is false. I stay neutral. Don't get emotional, and don't have an "I don't give a fuck" attitude either. Act worried for their well-being. I keep asking questions to make them fumble. My goal is to label them as liars. When they try to change the topic, I resist. I listen to what they say and make them repeat it, even if I heard it the first time. They will fumble when repeating if you hold your frame and make it seem like they are saying something outrageous. I think it's the way I look at them. I let them talk for a lil bit and say, "Wait, wait, wait, did you just say...?" and point out how it's false. Just keep asking them questions after questions and make the topic about them. Also Gaslighting. Never getting emotional. If your sitting somewhere minding your business and someone comes and says some shit to you this trick works most of the time, Just a loud “EEEEHHHHHHHH?” will

I could list all the tricks I use, but since I use them unconsciously, it's hard to write them all down.

Arguing like a lawyer requires you to know the logical fallacies and how people use them to win arguments.