Why is government regulation of airlines considered a controversial issue?

[Rupert]

The reason is that airlines are a business.
If the government regulates businesses, then they infringe upon free trade.
Most conservatives believe that the government has no right or authority to regulate business, as the constitution does not grant them any power in that area.

The two sides would likely be this:
Government should not interfere with business.
Versus
The government should interfere and regulate airlines because fair prices are important in our economy, and some regulations deal with safety issues.

I myself feel that the government should regulate airlines. I also would say that they do have constitutional authority under article 1 section 8 of the constitution: To make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers, and all other Powers vested by this Constitution in the Government of the United States, or in any Department or Officer thereof.
This is often referred to as the necessary and proper clause, and is why the government should have the right to regulate the airlines. Because it is necessary and proper to keep things from getting out of hand financially in our current economic climate, and to make sure they aren't cutting corners to save money that can lower the safety of those traveling on their planes, and those below, since a crash is a threat not only those on the plane.