no "he or she"

• You're using three words when you could simply use just one.
• You're excluding those who just don't fall under "he" or "she".

it's clumsy

Singular they has been used in English as early as the 14th century, including writers such as William Shakespeare:

There's not a man I meet but doth salute me
As if I were their well-acquainted friend

- The Comedy of Errors, Act 4, Scene 3

In the 18th century, people began to claim that it was grammatically incorrect - yet it always remained in common use:

As is well known, the popular solution to the problem, favoured by speakers and writers since early Modern English times, has been to use a so-called 'singular they',...thus sacrificing strict grammatical number concord in favour of gender concord.

- John M. Kirk, 2000

The pronoun they is commonly used as a 3rd person singular pronoun that is neutral between masculine and feminine. It is a convenient means of avoiding the dilemma of whether to use the he or she form. At one time restricted to informal usage, it is now increasingly accepted even in formal usage, especially in [American English].

- Randolph Quirk, 1985

If you've grown up speaking English, you have probably even used singular they yourself, though you may not know it.

not everyone is a "he" or "she"

Unless you don't go outside or this is your first time on the internet, you should already be aware that gender identity is a spectrum.

While most people use pronouns typical of their assigned gender at birth, many people don't. Some prefer others, use "they" to refer to them instead. Others identify more with neopronouns (pronouns outside of "he", "she", "they", or "it").

When referring to specific people directly, it's always best to use the pronouns they prefer. But to refer to someone not specific, or anyone else with an unknown or unspecified gender, use they rather than "he or she".

it is grammatically correct

Many influential organizations are already on board with singular they when used to refer to an individual of unspecified gender.

The MLA Style believes in this use of singluar they, so does the Linguistic Society of America.

This usage is also included in both the Merriam-Webster Dictionary and the Oxford Dictionary.

But no one organization is the authority on what is and isn’t correct. The English language does not have just one set of rules. Languages are defined by how they are used by people.

TL;DR

Using “they” rather than “he or she” has been common for centuries. It's more inclusive, and if that doesn't matter to you, it's also just one word compared to three.

Also it just sounds better and less clunky.