Likes ...
Mosque
Wick
Ace
Age

Kim
Akeem
Soy
Geese (& Goose)

Mice (& Mouse)
Mask
Mews
Quick

Yoga
Gay
Meows

But Dislikes ...
Church
Candle
King
Beauty

Dave
Abu
Beef
Hens

Cats
Cape
Barks
Slow

Dance
Straight
Purrs

My friend likes words that are made up of only the
thirteen odd-numbered letters of the alphabet:
A C E G I K M O Q S U W Y