Why do people use they/them pronoun for a single person?

I see a lot of people using they/them pronoun on their twitter handles. And when I googled about it, I have come to know that it is a Gender-neutral pronouns.

However, isn't it wrong to use words like 'they' and 'them' for a single person?

For example, when talking about such person, one has to say,

They are walking down the road.

which makes it plural. However, for a male/female pronoun, one can say,

He/She is walking down the road.

Answer

First, the singular they has been in use since before English became modern English; it was used in Middle English in the 14th century. It only became déclassé around 1900 when some overly stuffy grammarians started acting up.

Second, its use as a gender neutral singular is a bit more complex: It can be used either when we don't know the gender of the person:

Someone's coming up the street! They are coming to our house!

or when the person is nonbinary and prefers "they". Nonbinary people vary in which pronoun they prefer. Some use he or she, some use e, some use they; there are other possibilities to. Many prefer to use their names whenever possible, and eschew pronouns as much as possible. For instance, if the person's name is (say) Basil (as one nonbinary person I know is named):

Basil is coming up the street! Basil is coming to our house! Now Basil is knocking on our door!