How do you explain his big lie to Buffy in terms of motivation?
I presume you mean the 'kick his ass' lie?
Firstly we have to remember that Xander did let everyone else 'try it their' way regarding the re-ensoulment spell. He objected to it in the strongest terms, was over-ruled by everyone and so he let it go.
The result was that Kendra died, Willow almost died, Giles is now being tortured and Buffy is wanted for murder. That's the result of the first failed attempt, in his mind. Not exactly worth it to get dead boy back
So
Xander's thinking is that this second attempt that Willow wants, with the whole world at stake, maybe that shouldn't happen. So Xander makes a split-second decision not to tell Buffy about the spell.
So his motivation is not about killing Angel, its about playing it safe with the world at stake. I understand that motivation.
And I
HATE it, I hate what he did and that he
got away with it for so long. I hate that he didn't really seem to regret saying it until maybe S7. I certainly think his getting away with it unchallenged meant that he would try something
worse in S3 Revelations, and get away with that as well. I hate that.
I hate that the big lie probably cast a shadow of Buffy and Willow's friendship regarding Angel for who knows how long. I hate that its probably a part of the reason Buffy left town after sending Angel to hell. Because she felt that Xander, Giles and now 'kick his ass' Willow could not understand her pain, that her very compassionate best friend had been cheering her on to kill the bad guy who she once loved. Buffy had to carry that on her own for years.
So I get it and I hate it.