Why did Edmund lie about Narnia?

Lucy first comes back from Narnia at the beginning of chapter 3.  She is wonderfully excited about her recent adventure, and she assures her siblings that she is just fine.  They wonder what she is talking about, and Lucy tells them that she has been gone for hours and hours.  The siblings don't believe her.  It has been hours in Narnian time, but it has only been a few moments in real time.  Already at this point, Edmund is giving Lucy a hard time about her wardrobe experience. 

"But I've been away for hours and hours," said Lucy.

The others all stared at one another.

"Batty!" said Edmund, tapping his head. "Quite batty."

Edmund continues to antagonize Lucy for the next few days.  

The others who thought she was telling a lie, and a silly lie too, made her very unhappy. The two elder ones did this without meaning to do it, but Edmund could be spiteful, and on this occasion he was spiteful. He sneered and jeered at Lucy and kept on asking her if she'd found any other new countries in other cupboards all over the house.

Edmund will eventually end up in Narnia himself during this same chapter.  He will meet the White Witch and strike his evil deal with her.  Lucy eventually discovers that Edmund is in Narnia, and the two siblings return together.  Lucy is ecstatic that Edmund can corroborate her story, but he lies about it instead.  

And Edmund gave a very superior look as if he were far older than Lucy (there was really only a year's difference) and then a little snigger and said, "Oh, yes, Lucy and I have been playing - pretending that all her story about a country in the wardrobe is true. just for fun, of course. There's nothing there really."

I think that Edmund lies about his time in Narnia for a few reasons.  First, he wants to seem older and more mature than Lucy.  Admitting to something so unbelievable will make Peter and Susan think he's just as childish as Lucy.  Second, Edmund was so awful to Lucy about Narnia that he's now having a hard time admitting that he was completely wrong.  Third, Edmund doesn't want to admit much about his time there, because he might be forced to reveal his time with the White Witch.