"I do not consider myself either immoral or irrational, but I still can't see why human beings are necessarily significant. Of course, we consider ourselves significant, then our families, friends, communities, nations, and eventually mankind as a whole, in that order, but these are existential choices, not intrinsic properties. This is a prejudice we inherited from our ancestors, not a law of physics. If our ancestors had not felt that way we would not be here."

Well, some people think there is something more significant than humans and they call this God.

There may be something as significant or more significant than humans, but I'm not aware of it. As of this moment.

"I feel people are more important than say, whales, because I choose to feel that way. I also choose to ally myself with others who feel that way. I'm sure the whales feel very differently about it. If we consider the possibility of intelligent creatures from other worlds, the whole moral argument collapses and all that remains is racial chauvinism. Who is to decide which of two intelligent species is more or less wothwhile, or important, or valid. The entire concept is ridiculous."

Well, if we discover intelligent creatures from other worlds, then why couldn't they be as equally as significant as humans?
And returning back to Earth, if we were smart enough to be able to talk to whales, it seems to me that whales would become more significant- assuming whales were actually more intelligent and/or had more of a "culture" than the apes we have made some elementary attempts at communicating with.
But since whales aren't currently speaking English, at the moment, I don't regard them as more significant than humans. And I will be duly impressed if the Aliens master our language before we master theirs [if they use a babel fish, that is cheating].

"There is no reason why life cannot be worthwhile and fascinating even though it is strictly reductionist and mechanical. After all, a chessboard is very simple, the pieces are only a few in number and type, and the rules are easily learned by even a child. This does not mean the game is incapable of great complexity and beauty."

Assuming somewhat intelligent humans are engaged in this activity- for instance, monkeys and a chessboard are less complex and beautiful.