Why does the United States openly support some protests while opposing others?

Well, i think United States government are opportunist. They simply support something that benefit them.

USA had never openly support any group in Iran , it is an internal affair of Iranian people, no need for USA to get involve, their people are smart enough to solve their own problem ever since they over thrown Shah of Iran and occupied America embassy in Tehran. USA is only get to bear witness to the butchering of their protesters by the present regime , the republic of Iran and their president is too strong for the western power except UK.

For the same reason Obama encouraged and supported ACORN protesting and harrassing executives who got bonuses from the "Bail out" money, but openly made fun of protestors at the TEA parties.

I would have to say that it's because in Iran a dictator stole the election and in Honduras a dictator was tossed out. Obama wants to make sure that he gets Hugo Chavez' birthday gift to him delivered on time. Chavez plans to give him one of Lenin's books. The US seems to be going back to the policy of being kind to our enemies and punishing our friends. It may also be that in the case of Iran, Obama waited to see the polls to find out which stance the American people would like best but in the case of Honduras he wanted to see what Hugo liked best.

Can I say the one answer that my MIL would say............ OIL. Iran has Oil & perhaps a few terrorists. Honduras has what? Bananas? Produce? (sorry if I"m ignorant of what they have to export, but OIL seems to be a theme amongst the countries we've stuck our nose in)

It's easier. It's easier to yell at someone and tell them what to do and voice your disappointment in them if they'll just sit there silent. It's like that @$$hole guy who goes home and kicks the dog because he doesn't have the balls to stand up the people who are making him angry.