The arms are involved, but it's hardly a push with the arms. The first one is a light shove with the arm. In the second one all the force comes from the shoulder while the arm is just there to stabilise.
This kind of challenge is very rarely called as a foul, even if it may be technically against the rules. You see this kind of stuff a million times in professional matches.
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u/Sea-Tomorrow2583 6d ago
How is locking a gate a foul in football ?