What is wrong with this sort of talk? That is, what happens when you analyze it?
Not all truth is relative. The sun burns on hydrogen fuel. This is the truth regardless of whether or not someone believes it. A fish cannot live in my spare bedroom without water. The universe is full of such truths. While we can interpret things differently in terms of their effects, results, etc. , we cannot change the fundamental truths.
The answer to this question depends on who is being asked. On one hand, it becomes logically difficult to defend such a position. If we take the relativist stance literally, it means that there can be no absolutes and that everything is contingent on different elements. However, if "everything" is relative, then an absolutist statement is being made. Hence, it becomes logically inconsistent tao advocate a pure form of relativism. At the same time, it might become ethically dangerous to give credence to everything under the sun. For example, child abuse and sexual assault cannot be deemed as "relative." The cruelty inflicted by government and person cannot be seen as "it is only true for me." There might be a danger in speaking only for "myself" and not being able to advocate some level of pluralistic values that have to be accepted in order for some level of consensus to be reached that allows for a full embrace of all the levels of difference that is present in consciousness.
There's nothing wrong with this kind of talk. In fact, philosophers have been talking like this for centuries.
More specifically, the Danish philosopher Soren Kierkegaard says there are two kinds of truth: objective and subjective. For Kierkegaard, objective truth is characterized by outwardness, while subjective truth is characterized by inwardness. He says the objective thinker finds truth by approximation, while the subjective thinker finds truth by appropriation (acceptance of the condition of uncertainty), namely faith. He calls faith a state of objective uncertainty in which the individual affirms his or her own subjectivity.
Thus, when someone says, "It is true to me," even when others outwardly disagree, he or she is making a "leap of faith." Kierkegaard calls this an "either-or" situation, that an individual may disagree with the group objectively by asserting his or her own subjectivity.
All this is to say that truth is a paradox: it is both objective and subjective. You really can't split the two. They are flip sides of the same coin.
I do not know that there is anything absolutely wrong with that kind of talk. What I would say is that it has ramifications.
The most important ramification of relativism, in my opinion, is that there can be no right and wrong in this sort of a philosophy. If you are truly a relativist, there is no basis for saying that someone is doing something wrong.
If you are a complete relativist, you cannot even truly condemn Hitler. You can only say that, for you, it is wrong to kill millions of people simply because of their ethnic background. You cannot actually say that it is truly wrong to do that.
In addition to what has already been said here, I would like to note that this paradox is a truth in itself due to the bicameral nature of the human brain. Both the rational-logical and the spacial-temporal halves must work in balance to have sanity. This is where our many paradoxes come from. As long as we have balance we have paradox.
It is also called pluralism, the ability to hold opposing thoughts simultaneously. This is a mark of a free-thinking person. An absolutist thinker tries to strip away one side or the other, thus cannot find balance.
Take a look at the yin/yang symbol of balance. Note that the line is fluidly curved not rigidly straight. Life ebbs and flows.
Let me ask you something. If there were an absolute, objective, universal truth... would it not be outside of human experience? If so, would it not literally have nothing to do with us? How could we even know of its existence?