touch
牴 centers on physical contact: touching or coming against something. The meaning is narrow and concrete, without strong abstract extensions.
牴 combines 牜 (cow) with 氐, which likely contributes the sound and may relate to pushing or butting. The exact historical development is uncertain.
A cow (牜) uses its head to touch or butt against something (氐). Picture a cow gently touching a fence with its nose.
For テイ, imagine a cow touching a table (テーブル) with its nose: the 'te' from table cues テイ, and the cow makes contact.
disagreement; conflict; clash; discrepancy; inconsistency