It's a direct competitor (kill shot) to the UEFA Champions League. On its own, or as the big clubs see it, there's no problem. The founding 15 clubs are the most marketable, they can invite the hot clubs of the moment, gain the same eyeballs and get more of the money for themselves which will make their clubs better, keeping them at the top of the heap. Capitalism in the raw.
The problem is that UEFA, and by extention, FIFA run the champions league. The money, goes to fund global soccer. Smaller clubs, smaller leagues, lower divisions and domestic leagues in smaller nations. That's the window dressing, it's about money, and who receives it.
The other problem is that currently you have to earn your way into the Champions League, Europa league, etc. While many of these 15 clubs are UEFA tournament regulars, 5 of the EPL 6 are almost always in them most years, these clubs are no granting themselves a permanent seat at the table.
This has trickle down implications for the domestic leagues, especially the EPL. These clubs will now have resources that dwarf the domestic competition by a factor greater than they do currently at a multiple that would make the SEC/B1G blush with envy. It would effectively kill the prospects of any team making a legit run at a title, league cup or FA cup. The Leicester City or even Man City before they were Man City from winning. These domestic cups are essentially playoffs. If you can't win the league, winning a trophy is still a very big deal in European soccer.
The FIFA and the have nots are fighting back by threatening to excommunicate any clubs or players who join the new league from global soccer, incl the world cup and the domestic leagues.
It makes the CFB realignments from 20 years ago look like a school yard staring contest.