"Each person has ..." "Each" is a singular noun. When we use "each" we are considering people one at a time, so we use the singular. It's something like saying "One out of a million is ..." Even though there's a set of a million to choose from, at the moment we're only discussing one.
We don't say "each person have its ..." We don't normally use "it" to refer to people. People are "he" or "she" or "they". There are just a few exceptions to this for unknown people. Like if someone asks whether an unknown person is male or female, we may reply, "It's a man" or "It's a woman". Though we more often say, "He's a man" or "She's a woman." We also sometimes use "it" in questions about an unknown person, like "Who is it?"
As Damkerng says: There's an old convention that when the gender is unknown, use the masculine. So you would say, "Each person has his ..." if the group is male, is a mix of males and females, or is known. You would only say "Each person has her ..." if the group was all female or was a group that is normally thought of as female.
Using the masculine for both male and female is considered sexist by some, so now it is common to say "he or she", or to use "they" as a singular pronoun for a person of unknown gender. "Each person has their ..."