Is there any reason why Agility is type Psychic?

Question

There are other moves like this too.

Answer 1

The user relaxes and lightens its body to move faster. It sharply boosts the Speed stat.
that is the move description in BW 2. maybe it does that with its mind and willpower

Answer 2

Bite is evil!
Razor Wind should be flying though
Agility is learnt by many Pokemon (non-psychics too) so... I guess it is because of super speed can be controlled with psychic, I guess..

Answer 3

Tackle a ghost it has no effect
Bite a ghost its supereffective

But in all seriousness, Agility is described as being a 'Special Technique" in Stadium, and from FireRed/LeafGreen on, it is described as lightening the user, so in this way, it is mystical.

Finally, Generation One is notorious for its oddity regarding types (The abundance of powerful normal type moves in comparison to other types, such as Bug, and the classification of moves such as sand attack, gust and karate chop as normal attacks for example). Psychic types also got set-up moves in all stats (meditate, barrier, amnesia and agility) in gen 1, so that could mean something.