Is there an answer to the question why there are only four fundamental interactions of nature?
No, and there never will be one
We have no science at all which can answer any meaningful "why" question about the structure of the universe, especially not about why things we do not observe are missing.
The best we can come up with is to observe a bunch of features and figure out somewhat fitting mathematical/physical theories about how they might be interrelated. And we get that wrong all the time.
My word "meaningful" up there means going down to the "lowest turtle" when explaining something; i.e. not simply an answer which stems from theories we have which seem to fit our current understanding of nature.
For example: we know that nothing can go faster than c
mainly because according to Einstein, it would take an infinite amount of energy to get something with mass even up to c
, not to mention faster. But this is, in the sense of this answer, not an answer to the question of "why can nothing go faster than c
?". I interpret that question as "Why is our universe structured in a way that you need infinite amounts of energy to get to c
?".
In fact, on any given day someone might find an error in our theories and figure out a way to move faster than c
, or do time travel, or find a 5th fundamental interaction. As we cannot even know anything about the universe with absolute, fundamental security, we can certainly not answer a "why" answer.
A very nice video about this: Richard FeinmanFeynman. Why.
So I am not going to be able to give you an answer to "why magnets attract each other?" except to tell you that they do, and to tell you that that's one of the [...] different kinds of forces [...] [...and to give an explanation in more difficult terms...]
This is not exactly the same kind of thing we're talking about here, but should show the spirit when answering "why" questions.
Outlook
This is a fascinating topic, and you could do worse than checking out the antrophic principle and the moat of philosophical topics hidden behind that. This principle comes in two versions:
- The strong antrophic principle basically says (my wording) that the universe was tuned "just so" to enable intelligent life (us!), i.e. with intent.
- The weak version says "if the universe were not able to sustain life like ours, we would not be here to ask the question".
The strong version veers right into the direction of beliefs and religion, and while for many people it may be valid, it certainly is not really applicable here on Physics.SE (and while there may be believers amongst physicists, it certainly does not give us any new information).
The weak version is obviously true, and it leads to a bias about what features our universe must have. But it also does not answer any kind of deep, substantial "why" question.