How about if I'm well off and still want to bitch about the poor getting poorer?
I've studied reasonably hard, got a reasonably well paying job and have invested reasonably smartly. I have perhaps more than I need and think that I (and others like me) should be taxed more to give those born in less fortunate circumstances the opportunity to better themselves (the same opportunity I've had when I was growing up).
As others have said, it's all about what type of a society you want to live in. Personally, I don't like the idea of gated communities, or having to send my kids to private schools. That's why I try to do all I can to support a greater middle class. And that includes accepting that I should pay more tax.
Not so it can be handed out in welfare to second or third generation unemployed mind you, but to give their kids the education and ability to create a better life for themselves. The wealthy benefit from an (IMHO unfair) tax system, which often encourages parasitic investment of capital. Negative gearing is my personal pet hate, but there are plenty of others (salary sacrificing, GST, tax deductions for (questinable) "business" expenses and so on).
At the end of the day, we're all interconnected. If 10 people have to struggle on minimum wage so I can make more money that I don't need, it will adversely affect my quality of life in the long run. It will mean ten less people that use the goods or services I produce, might mean two or three more people that are looking to rob/scam or otherwise cheat me, etc etc...
... long story short, if you've made something for yourself I think that's great for you, especially if you didn't start with much. Sounds like you were able to utilise some government provided services to get there, and that's great also. Unfortunately, there are fewer opportunities for people from lower socio-economic backgrounds to make something of themselves today then there were 10 years ago, and fewer still than there were 30 years ago. And that's in large part because our taxation policies are skewed to help the wealthy get wealthier, thus leaving a smaller slice of the pie to be fought over by a greater number of people.
And in my humble opinion, that's not fair!

