Why would I waste any energy on upsetting myself over such nonsense?

Only one thing matters: do they have a point or not? Everything else is decoration and should have no impact on your decision making process. If you don't understand this you're not sufficiently mature to operate in society without hurting yourself and those around you.

First off all, you have the capacity to gain full control over your emotional and mental state. This is hard, but if you want to feel constantly euphoric, depressed, angry or anything, you can do so. Actively.

Secondly:

• If someone insults me with random terms, then that gives me no reason to change my emotional or mental state. They've merely made some sounds, without changing anything about my life.

If someone insults me while making an argument, then either:

• They have a point I have not yet considered and can now decide to which extent I incorporate the new insight into my life to grow as a human being or
• they have a point that I have considered already and don't care about or
• they have a point that I have considered and concluded to be false, hence irrelevant.

In none of the potential cases is there any reason for me to change my emotional or mental state.

Either I decided I don't care about their point (because they're wrong or it doesn't matter) or I incorporate their points and ignore the "offensive" language that was used to embellish the point they tried to make.