[quote=@1Charak2]
<Snipped quote by Cu Chulainn>

If his powers are by association which he denies due to his devout Catholicism. Then half of his stuff makes no sense and seems tacked as it conflicts which his denial of god hood. 
[/quote]

After doing research on all canon Heroic Spirits who do have Divinity, I believe I have to correct myself. It's not even a denial of his supposed godhood, if we're being technical. His divinity isn't speculated, it just isn't there. He isn't a divine spirit, nor is he related to one, nor is he worshiped in the way a saint is. There aren't any cults to Pedro de Alvarado, and his skills come from what the natives saw him as. He never ascended as a divine spirit, and if he did, then pretty much all foreigners/conquistadors of his time should be divine spirits then, since he isn't the only foreigner that could have been mistook for a God due to his foreign looks.

He's not a god. He's not part god. He's not [i]worshipped[/i] as a god. No real aptitude for Divinity. He's just drawing on the power of the legends where he's associated with the Sun God, just like how other Heroic Spirits draw upon their own legends to produce their various abilities.