'A part of' emphasizes "a part of many."
'Part of' emphasizes "belonging," without saying anything about the number/multiplicity of parts.
A part’ is a singular count noun:
• A part of something is one of the pieces, sections, or elements that it consists of. (In this case, perfection is one of the many parts of being human)
Part is a noncount noun:
• If something or someone is part of something, they belong to it or are included in it. (In that case, imperfect is included in being human/ in the human experience)