The opposing force comes from the object pushed away from you. Consider:
What is the difference between pushing an object away from you with your legs, and jumping off that object?
If you were in space, in free fall, and asked to do those two tasks what to you do differently? Besides your point of view they are the same motions and the same result.
Now light having momentum is a bit weird since it has no mass, but I don’t think that is central to this question.
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