This is quite a common question. I can understand where you come from and believe that your confusion originates from not discerning Newton 2nd law and Newton 3rd law.
Let talk about your question. Call the force that you exert on the door be
while the force that the door exerts on you be
From Newton’s 3rd law, we note that
what is important is to note that the force is exerting different “object” NOT same “object” as mentioned by many others.
To decide whether the object “moves” or NOT, we need to use Newton 2nd law. Sum all the forces that exert on that object vectorially:
Apply Newton 2nd law to the door:
Note that we are summing the forces that exert on the door NOT the force that the door exerts on another object.
Apply Newton 2nd law to the you:
Similarly, we are summing the forces that exert on You NOT the force that You exerts on another object.
Do you see any cancellation of the two forces?
Hope this makes sense to you now.