Herbert Dingle also pointed out this problem: that the relativists seem to want the time dilation to be both symmetrical and asymmetrical between observers; where each observer says the other person's clock is slower (i.e. time dilation symmetry) but then mysteriously only one clock becomes slower (asymmetry). The relativists seem to want their cake and eat it too.
you can't have your cake and eat it too: This phrase is easier to understand if it is read as "You can't eat your cake, and have it too". Obviously once you've eaten your cake, you won't have it any more. Used for expressing the impossibility of having something both ways, if those two ways conflict.