I personally have multiple reasons, but first I'll address your reasons.
* Your beliefs really don't matter too much to me. For example, I'm from a family in which my mother is a pantheist and my father is a Catholic. I am a skeptic, but my siblings are too young to decide yet. Fortunately, my parents - primarily my mother - allowed me to develop my own set of beliefs based on what I felt is right, and I would never deny anyone that opportunity as long as their beliefs do not harm others. I believe in freedom of choice. I am going to educate my siblings, but if they choose a different path, I'm completely fine with it.
* However, I also believe in educating others to enable them to make an informed choice. In my eyes, skepticism is asking questions of "accepted dogma" and "perceived wisdom," but only on the basis of evidence. It's not wrong to ask questions - the greatest scientific discoveries are made by asking questions about the world - but you should inform yourself before you do ask questions.
* The reason that I do not reveal my name on websites is because I am a minor, and my mother does not allow me to. When I am no longer a minor - about a year - I may choose to reveal my name on the internet. I have no problem revealing my name, and I do not fear ridicule. There are safety issues to revealing one's name on the internet, however, which is why many people choose to go by a forum handle instead.
* I am openly a skeptic, so the issue of "coming out" does not apply to me either. My friends know this and my family knows this. I'd imagine most skeptics are not closeted, either. The problem with the concept of "openly being a skeptic" is that it doesn't really apply to day-to-day life. I am openly an atheist - I don't attend church or religious services, and I will mostly opt out of religious activities. However, thinking critically is really just an aspect of who I am as a person, equivalent to saying that I openly love strawberries or openly a classical music fanatic.
Here are my reasons.
* Irrational beliefs can be harmful, both to the individual and society at large. Check my signature for a link to a website keeping a tally of the damage pseudoscientific thinking has done to the world.
* I believe individuals should have the freedom to make their own choices in life, but their choices should be informed choices, based on the evidence we have of the world. Hopefully, I can educate people, point out the flaws in their reasoning, and allow them to make informed choices in the future. I can only hope others will return the favor in kind.
* The reality of what exists, based on evidence gained from the hard work of millions of people over thousands of years, is far more wonderful than most people can comprehend in a lifetime. Miracles, pseudoscience, and other paranormal beliefs sort of seem cheap in comparison to the wonders of our world, and I hope perhaps I can open up this opportunity for others to experience it as well.