Who's against the Big Bang? And why?

You can get some hints here.

From this so-called "cosmology statement":

The big bang today relies on a growing number of hypothetical entities, things that we have never observed-- inflation, dark matter and dark energy are the most prominent examples. Without them, there would be a fatal contradiction between the observations made by astronomers and the predictions of the big bang theory. In no other field of physics would this continual recourse to new hypothetical objects be accepted as a way of bridging the gap between theory and observation. It would, at the least, raise serious questions about the validity of the underlying theory.

Unfortunately, they don't bother pointing out that several independent lines of evidence lead to the conclusions about dark matter, dark energy, and inflation. The underlying motivation of many of the signers is subtle, but it pokes out momentarily:

Yet the big bang is not the only framework available for understanding the history of the universe. Plasma cosmology and the steady-state model both hypothesize an evolving universe without beginning or end.

Oh yes, that troublesome beginning of the universe that comes with that big bang. Philosophy and theology (or lack thereof) drive most objections to the big bang. However, objections to the big bang often make odd bedfellows. Take, for example, this set of names of signers to the statement:

Harlton Arp
Hermann Bondi
Thomas Gold
Eric J. Lerner
Jayant Narlikar
Anthony L. Peratt

Those are just some of the physicists and astronomers' names I recognize. They all don't like the big bang because they have philosophical objections to the universe having a beginning (especially Lerner). However, there are another couple of names on this list that I find interesting:

John Hartnett
Charles Creager Jr.

These guys are both young-earth creationists. The big bang bothers both atheists who want an eternal universe and young-earth Christians who want a young one.

And of course both groups are claiming that they don't get a fair hearing and that the research is skewed. This isn't really fair either. Some of the astronomers on that list were prominent scientists who made valuable and important contributions to the field, and without their poking and prodding at cosmology we would have never refined the big bang theory. And, of course, young-earth creationists have no shortage of money and attention.

Anyone is free to put forward any model of the universe they choose to be subjected to testing. The facts, however, seem to again and again point in the direction of a big bang universe.