Problems with Relativism

I just now saw the following post:
https://steemit.com/philosophy/@lukestokes/what-if-there-is-no-big-t-truth

This is the latest article I've seen about this concept called "relativism" which essentially states that people can disagree about anything and nobody is more correct than anyone else. Earlier today I heard a story of someone who had a disagreement with someone, to which they responded, "That's just my opinion and opinions can't be wrong."

Being a mathematician and logician, this sentence makes me cringe because I know that the implicit and sometimes even explicit first rule of logic is that contradictions can't be tolerated.

The reason we need this "law of noncontradiction" is that, without it, our words are meaningless...sure you can say that there's no real truth, but then you're giving up any right to object to injustice...you're giving up any right to object against anything because you've already declared that their opinion is just as valid as yours.

You can get mad...but you must then acknowledge that your anger is illogical!

The most blatant problem with relativism, though, is that it defeats itself...

I can easily claim relativism is false, I'd be making a truth statement from a position where they can be made...
However, if you try to claim that relativism is TRUE, then you're making a truth statement from a position where you've already disqualified all truth statements!

You're saying, "Objectively, there is no objective truth." without realizing that that sentence applies to itself!

In other words, if you believe subjectivity, you can't defend it or even claim to be more correct in believing it!