The Japanese language we use includes kanji, hiragana, and katakana. First, let me explain about Kanji.
Kanji is a character originally used in China. Since Japan did not have any writing in ancient times, the Chinese characters were used as they were in China, which is located next door. For this reason, more than 1,000 years ago, Japanese texts were written only in kanji. At that time, however, there was a kind of rule that only men were allowed to use kanji. Such a distinction is completely unthinkable today, but it was the norm in Japan more than 1,000 years ago. In that case, women could not even write letters if they only had Kanji characters. Therefore, women began to write letters using characters that were not kanji, by breaking down the shapes of kanji characters. This was the beginning of hiragana and katakana.
It is impossible to say exactly who created them and when. In this way, hiragana and yakata kana gradually came to be written.
By the way, it seems that women of that time often wrote love letters. This was because it was an era without telephones, and the only way to confess your love to someone you liked was to write a letter. Naturally, men who received love letters would receive letters written in hiragana or katakana. This led to men also using hiragana and katakana in their replies to love letters. This is how hiragana and yakatakana came to be used by both men and women alike.