Paradox #1
Some people see a contradiction in Matthew 22:44 because it presents a conversation where David calls the Messiah "Lord," even though the Messiah is supposed to be David's descendant. This confuses the hierarchy of authority and lineage because typically, descendants would not be considered greater than their ancestors. This can lead to questions about the nature of the Messiah in relation to David.
Paradox #2
The potential contradiction in Matthew 22:44 could be the idea of having enemies that are to be made a footstool, despite other teachings of love and forgiveness. Jesus also teaches to love and forgive others, even enemies. This could seem inconsistent because it suggests dominance over enemies instead of making peace with them.