Terminology of speaking mannerism

In linguistics, expressions such as

but that’s just me
I'm not telling you what to do, but…
I didn't say anything, as it’s none of my business, but…
but that's just my opinion
but what do I know?

are called hedges, in your examples following a reversible pattern of

Hedge, but assertion
Assertion, but hedge

This type of device lives on the force of the contrastive conjunction.

Hedges are a kind of euphemism employed to soften the impact of an utterance the speaker feels might be too confrontational, demanding, or impolite, that is, socially transgressive in some way.

Australian business consultant Corrine Armour crafts a paragraph to illustrate:

Stuffing your communication with hedging words making no contribution to your message is a linguistic crime that decreases your ability to influence.

Allow me to demonstrate: ‘Basically, what I’d like to do is to tell you all about hedging. I guess I think it’s really important. The point is, hedging can reduce the authority of your words, and basically I feel it reduces your power. In my opinion you shouldn’t really let hedging into your conversation, because I just think your subconscious mind hears it too and the point is you will feel less confident.’
…

If you think the first example is exaggerated I invite you to listen to people around you, and possibly yourself.

Since Robin Lakoff’s 1973 monograph Language and Woman’s Place, there has been a spirited discussion whether women speakers hedge more than men, and if so, why they do and under what circumstances.