The correct pronunciation is mi-thinks - short i vowel sound. A change in pronunciation may pacify the teacher.

Audio here: https://www.merriam-webster.com/dictionary/methinks

Also, he might enjoy vocabulary.com. It's a free platform to learn new words (and spelling!). There are thousands of lists already, or you can make your own list from whatever he is reading. My son likes to practice spelling words there and I love playing on the GRE vocabulary lists. So many words! There is audio for correct pronunciation too. There might be a word list for Shakespearean insults. 😇