I'm learning hiragana . While I am learning the letters , do I have to memorize the words as well or should I just keep reading them? I have been reading it since I first started.
The words are just examples so you can see the kana in context. If it helps you to remember the words alongside the kana, study them. If they don't help you, don't bother.
You can memorize the words but they are just examples, But if you play shiritori cat they do pop up on the game. It's on you if you want to memorize them to help you understand each letter.
Sometimes you will get stuck on a specific character that your brain doesn't want to learn, learning it as part of a word can help get around that. Ex. You might get ち and さ mixed up but can remember a word like ちいさい
Same idea applies for kanji in words or words in sentences.
I have been reading it since I first started. 
