Intuition or analogy?

Neither, It's an assumption.

It's an intuition, a faulty inference, and an assumption.

* Intuition: a gut feeling that tells you what is true. Intuition is not always right, but it is right often enough to be tremendously useful.

* Faulty inference: an inference is where you derive a conclusion from premises. In this case the conclusion does not necessarily follow from the premises, so it's a faulty inference. For instance, the following would be a valid inference: "My parents are good in math, everyone whose parents are good at math is also good at math, therefore, I am good in math too."

* Assumption: an assumption is taking something as true without conclusive proof.

* Analogy: an analogy points out a similarity between two things. An analogy is not a metaphor or simile:

* Metaphor: calling an object another object, eg. "the sun is a yellow flower".

* Simile: describing an object as another object using the word "like" or "as", eg. "the sun is like a yellow flower".

It is neither, I would call it an assumption. You are assuming that you are good at math because your parents are.

However it is not a valid assumption because it does not necessarily follow that if your parents are good in math you will be to, or if you are good in math it is because your parents were.

An analogy would be something like:

"My parents are like a tree that shelters me and gives me the fruits of knowledge."

An intuition:

"I have a feeling my baby will be a great mathematician."

Probably an Intuition.

Intuition provides us with beliefs that we cannot necessarily justify.

Intuition is a combination of historical (empirical) data, deep and heightened observation and an ability to cut through the thickness of surface reality. Intuition is like a slow motion machine that captures data instantaneously and hits you like a ton of bricks. Intuition is a knowing, a sensing that is beyond the conscious understanding — a gut feeling. Intuition is not pseudo-science. (by Abella Arthur)

analogy

a similarity between like features of two things, on which a comparison may be based

you believe that since you are like your parents and they are good at math your ability at math would be comparable to theirs

It is called inference