it doesn’t mean both sides are bad in every single conflict

But you’re implying it. You’re implying far greater equivalence exists than there is.

If English isn’t your native language, then let me help you.

both sides are bad

Is wrong. That is a final judgement, and it is wrong

both sides have faults

Is correct, and what you mean. It still isn’t good, but is closer to what you mean.

Also, on the topic of left, right, centrist and moderates (etc), you should be aware of the concept of the Overton Window. (https://en.wikipedia.org/wiki/Overton_window) I am not going to support the entirety of the concept, but the basic relevance is that “if the general trend of the times is for people to be more right wing, then what you thought was central becomes what was right wing in the past”. This is a fault / problem with describing an idiology not on its own, but only in relation to others.

Language is used for communicating ideas and thoughts, and if you don’t use it “correctly”, in the manner that other people use it, then you will be misunderstood.