In my (uneducated) opinion, the specific problem is that the people, through their governments, lose control over these large, global entities that affect their daily lives. When they get this big, there's no way to tax them and no way to punish them for wrongdoing - they could just move to a friendlier country, use loopholes, etc. Of course, thanks to various trade agreements, they will still have access to our markets...

And the consumer can't always go elsewhere - there may be no viable competition, or that competition gets bought by the larger company for what is essentially pocket change.

Too big to fail = too big to control