After losing my faith in God, I was unsure about what should be my basis of morality. I discovered part of the answer in Sam Harris's
TED video on how science can answer moral questions, and his book
The Moral Landscape. The basic idea is that morality should be based on promoting human well-being, or in other words, based on empathy, compassion, and loving your neighbor like yourself. So I'm a big fan of Jesus's 2nd greatest commandment (although obviously not so much his greatest).
The traditional basis of morality is tradition, usually religious tradition. Using compassion as the basis of our morality means that it can progress, and there are several reasons that it might:
Tradition may be mistaken
There are a lot of commandments in the Old Testament that seem objectionable to us today. For example, most of us would consider it wrong to kill someone for collecting sticks on the Sabbath, for worshiping a different God than us, or for being the child of someone who worships a different God. I realize Christians don't follow those rules now, but were any of those things ever right? If not, then maybe we should question whether scriptures are a good source of morality.
Our environment may change
For example, as we become more and more exposed to advertising, and that advertising becomes better at causing us to want to buy things, we can re-evaluate its effect on our well-being. We may realize that advertising does not promote our well-being, and we should take steps to reduce our exposure to it. What's right can depend on our personal circumstances.
We may learn more about human nature
After we learn that sexual orientation is largely immutable, and that most gays and lesbians are happier accepting their sexuality than repressing it, we can become more accepting of our gay and lesbian peers, or even encourage them to accept their sexuality rather than repress it.
People are different
What's right for one person may be wrong for another. Maybe pre-marital sex is a terrible idea for some people, but fine for others, depending on their personalities, desires, and situation. Maybe getting married and having a family is a really great idea for some people, but not others. We shouldn't think that what's good for many people necessarily applies to everyone.
For these reasons and others, I think loving your neighbor as yourself is a superior basis for morality than religion or tradition.