Up until the 5th century CE, writing wasnt around in Japan. However during the 5th century the Chinese characters came to Japan from china. The Japanese originally planned to just use the characters in their writing. However, they soon discovered that the Chinese written language and the Japanese spoken language dont mix well together. Their solution was to keep the characters but use Japanese grammar in their writing.
Over the course of roughly 300 years the Japanese gradually adapted the Chinese written language until the Hiragana method appeared in the 8th century CE. However, there was still competition between Hiragana and Chinese. Men in power still used the Chinese language to write government documents. However, women started to learn hiragana becuase they werent allowed to learn the chinese characters that their husbands had. Eventually hiragana gained the upper hand and the split between hiragana and chinese ended when hiragana became the accepted form of writing.
Because of this segregation between men and women on their either choice or forced choice of literary script, many women wrote some of the best poems of the Heian era. When there was the first royally commissioned Japanese Poetry Collection, both female and male poets were able to submit their works to be published in this great collection. Along with collections there were formal poetry contests which were created to show the talent of poets. A topic would be announced in advance and the entries would be read aloud by an offical and then judged.