Usually -OH group (-OH group of serine, threonine and tyrosine) gets phosphorylate. Why can't other groups phosphorylate like -SH (thiol of amino acid)?
In theory the thiols could be phosphorylated, and indeed there are very few examples of phospho-S- compounds (see below). The same kind of question could be asked for Si : why C is used in chemical compounds and not Si, the 2 have similar electronic repartition on the outer level... however "something" made Si be the atom of minerals and C of life molecules. One of the explanations could be that the radius of the atom makes the links to be strictly oriented (tetrahedrical for CX4) or less well oriented... and also that the overlapping of orbitals is better if the orbitals are of approximately the same size (ie n=2, wether it is 2s or 2p). The same may be the explanation of the very little use of S instead of oxygen. in life molecules. Also the electronegativity of SI or S may not be adequately matched with that of other atoms. All of this implies that at the end the possible complex R-S- phosphate is not stable. Interistingly there are at least compounds where S and P are linked such as : phosphothiol, SPO3H3. Iin this S is doubly linked to P, and not on its thiol form.
However there are phospho-thiols in nucleotides (ATPalpha S, see articles by https://www.researchgate.net/researcher/7457287_L_A_Wozniak/
in bacterial and plants there are two-component phosphorelay systems consisting of a histidine kinase which usually autophosphorylates at a histidin residue and afterwards transfers this phosphoryl group to an aspartate of its cognate response regulator.