Before I can answer the question, I need to have some idea of what "nihilism" means in this context, because there are many different varieties of it. I assume this is the most common one, the one that proposes that life is meaningless and purposeless. If this isn't the kind of nihilism you're referring to, please correct me.

To answer the question, I'm not a nihilist because nihilism is conceptually mistaken.

For example, suppose there is a stick, a normal brown wooden stick of some length. Now, is that stick a meter long or not? Whether it is or isn't, that question is conceptually sound, because the concept of stick has the attribute "length", which we can compare to the length of a meter, Is the stick morally just? This question isn't conceptually sound, because "justice" isn't an attribute of a stick. A stick isn't just, unjust, or morally gray, it completely lacks the attribute of "justice".

How does this apply to life? If you ask whether life is meaningless, that presupposes that conceptually life can have a meaning in the same way a stick can be a meter long - that "meaning" is an attribute of life. However, meaning is informational - words have meanings, as do symbols and signals in general. When I say "apple", you can imagine an apple, or at least know what I'm talking about, which means that the word "apple" is meaningful to both of us. If I say "Colorless green ideas sleep furiously", it doesn't bring anything to mind, so that phrase is meaningless. Life lacks the attribute of "meaning", because it's not information that's being communicated. Therefore, to say "life has no meaning" is more similar to saying "the stick is unjust" than to "the stick is shorter than a meter".

That deals with "life is meaningless". How about "life is purposeless"? To answer that question, consider where purpose comes from - from using something to achieve a desire. For example, if I say "a hammer's purpose is to hammer in nails", what that really means is something more like "A hammer is well-suited for hammering in nails and is often used for that end". If I want to hammer in nails, then, for me, the purpose of a hammer becomes to hammer in nails. If I want to eat porridge with a hammer (something I don't recommend), then to me the purpose of a hammer becomes to move porridge from a plate to my mouth. You may assign the hammer either of those purposes, or an entirely different one. Each of us can even assign multiple purposes to the same object. The point is, purpose is not a property of an object on its own, but one that arises from it having a relation with a being that has some use for it.

So, when you ask "What, if any, is the purpose of life?" that question requires much clarification. The purpose of whose life, and to whom? Just as we can assign different purposes to a hammer, we can assign different purposes to a life. For example, the purpose of my life to me is to keep me around, as I wouldn't be able to experience things if I were dead. Other people may assign different purposes to my life. So, a life can be purposeless, but only if no one, including the possessor of the life, assigns any value to it (and that assignment of value is in a reflective equilibrium).

To summarize:

"Is life meaningless?" - "Wrong question, meaning isn't an attribute of life."

"Is life purposeless?" - "Purpose is subjective and assigned by beings with desires. It is impossible to make a blanket statement about life in general, but it is possible for a particular life to be purposeless, though it is unlikely. Most lives have at least one purpose assigned to them."