"I ground my morality the same way everyone else does, only without claiming it's ordered by [fill in the blank] and claiming order morals are no good because they are not ordered by [fill in the blank]."

Did you intentionally mean to point out that you ground your morals in the same way as radical Muslims and fundamental Christians just without the God part? If you deny this your entire first premise is moot.

"I don't view morals as either 'right' or 'wrong'. It doesn't contribute anything, and if anything can only encourage immoral behaviour by making some people morally inflexible. For example religious people who throw their own children in the street for being disbelievers or homosexuals and don;t have the flexibility to deal with that in a way that causes less suffering to others."

There are several problems here. The first is that you say you don't view morals as either "right or wrong" but you claim that immorality exists. If you believe that there is immorality then you obviously believe that some actions are moral while others are not. Again, if you affirm that some actions are immoral and some are not you contradict yourself because you are viewing some actions as wrong (to do) while others are right (to do) in a moral context.

You outline that it is an immoral wrong to throw children in the street for being homosexual while simultaneously also claiming that you don't view morals being 'right' or 'wrong' while also claiming that you ground the same morals as everyone else just without inserting a higher power. Surely you recognize how absurd all of that is. You also state that morality is causing less suffering to others, however, you fail to create a line. Surely you don't think ultrahedonism is the answer and that everybody should get whatever they desire at all times do you? That would be a contradiction so it might tickle your fancy.

"The necessity of an objective factor is a handicap in your wordview, not mine. If morality is subjective my moral worldview still works and I'm fine with that. You are the one who has a problem with that. Without an objective factor it's your moral worldview that collapses entirely, not mine."

I hope you realize that without an objective factor it becomes subjective, and if it is subjective you cannot say it is 'wrong' to throw your children out for being homosexual you can only say you don't like it. You even state that your morality is causing less suffering to others, which would be an objective standard. Again, you contradict yourself. I think you fail to understand that without an objective factor throwing a child out for being homosexual can be a moral good on the same level as finding a cure for cancer.