So in the journey of trying to understand more about the strong interaction I have encountered some passages linking mass with strong interaction. Like from Greiner and Müller Quantum Mechanics - Symmetries
Clearly, all pion masses (energies) are nearly equal. In analogy to the mass difference between proton and neutron, this near equality may be interpreted as meaning that the strong interaction (which determines the dominant part of the mass) is invariant in isospin space, and that the small mass differences of a few MeV are caused by the electromagnetic or other interactions.
Also from Griffiths Introduction to Elementary Particles I read
Apart from the differences in quark masses, the strong interactions treat all ﬂavors equally. Thus isospin is a good symmetry because the effective u and d masses are so nearly equal (which is to say, on a more fundamental level, because their bare masses are so small); the Eightfold Way is a fair symmetry because the effective mass of the strange quark is not too far from that of the u and d. But the heavy quarks are so far apart that their ﬂavor symmetry is severely broken.
Now I do not really understand why or how the mass depends on the strong interaction or vice versa. From Griffiths it seems, that the reason why isospin is not a good symmetry for higher mass differences is, that only "apart from the mass differences" strong interaction treats the quarks equally. I was not aware that strong interaction cares about mass. How come? What exactly is the relation?
Actually I have thought that strong interaction doesn't care at all about mass and so I find these passages really strange. In the case that someone could clear up that no, indeed strong interaction does not depend on mass, than I would like to have another explanation of why isospin is a worse symmetry for huge mass differences.
Personally I had the feeling that it is just because exchanging the particles with very different mass makes the Lagrangian not really symmetric anymore, but there is no word on that in these passages I have quoted.