Would it be possible to write a book and never reveal the second main character's gender?

You could refer to the person by their title, job description, or what they're wearing, e.g., "the person in black." You could also give them a distinctive quality to their speech, so that you wouldn't need to use attributions ("s/he said") when they spoke. For example, if they spoke with a deep accent, you wouldn't need to add "she said" at the end, since it would be obvious who was speaking.

Left Hand of Darkness by Ursula K. Le Guin is about a race of people who are sexless. I haven't read it, but that may be worth checking out.

The other person's comment about being clever is that such evasiveness would quickly be spotted by many readers. They would notice that you're deliberately not mentioning one person's gender and would see it as an attempt by the writer to be clever and trick the reader.

If you're going for a sexless creature, then it's simply a technical problem of what to call this person. But if you're going for a "Gotcha! This person was a woman/man all along!" kind of ending, then some readers are already going to be expecting that. Something to keep in mind as you write.

It's very possible if you don't want the character's gender to not be known, call him/her by a nickname or give him/her a general name that can go either way Like Alex it could be a girl or boy's name but we'd never know if it was a girl or boy

It's possible, yes. Arnaldur Indridason deliberately does this with one of his supporting characters in his excellent novel 'Jar City' (sometimes known as 'Tainted Blood'). The character's name is Marion Briem - the novel's set in Iceland where both those names are unisex, and never once in the whole novel does the author or any of the characters refer to Marion as 'he' or 'she', so we are left never knowing whether it's a man or a woman.

Obviously it's something you'd only want to do for a good reason (Indridason apparently does, as it relates to a wider theme in the novel) though, so I'm assuming you have one.

It would be better in the poiint of view of a character whose gender is never revealed, that would be really interesting.

Possible, yes. But what would be the point? The aim of a story generally isn't to demonstrate how clever you are.