Here we have a riddle, a statement written in a way that should tickle one's imagination and make them think through for a sensible answer.
Let's read the question again: Two doors are opening and closing at the same time, but they are doors of my house.
What are they?
Let us analyze the first part of that riddle. "Two doors are opening and closing at the same time" may be misunderstood, as the door is not simultaneously swinging open and close, but rather the two doors make the motion together."
...but they are doors of my house" here means that the doors are a part of something... a part of us.
Here, we can say that the riddle talks about a part of our body.
So, what part of our body comes in two and opens/closes at the same time? It's our eyes!As a side note, we could say our hands, but we don't always open and close them together, whereas those are the only motions our eyes can make.
We can close only one eye, but we don't always do that. In fact, we subconsciously blink our eyes a lot more than you think!