Fete and feat are easily confused words.
The spell-check application of most word processing software programs would not catch a slip-up of these two words. Spell-check is looking for words that aren’t in its dictionary, and words that resemble words in its dictionary but are possibly spelled wrong. Spell-check isn’t perfect. It doesn’t know and can’t guess what word you wanted or what word you meant, it can only judge the words on the page. If you used words that are all spelled correctly, it gives you a pass anyway.
Autocorrect suggests words that start with the same letters. It’s suggesting what word you may want to save time, but quite often, its suggestions are pretty off base. They don’t help you out, but they do make you laugh.
Fete (pronounced fay+t) is a noun. It means a day of celebration. It can also mean a major event. As a verb, it can mean to entertain someone important with this kind of celebration.
Feat (pronounced fee+t) is a noun. It means a display of extraordinary strength or other remarkable talent.
The following story uses both words correctly:
Faye wasn’t sure what feat she could perform at the school’s talent show. She never felt good at sports, music, or dance. But the teacher in charge, Mr. Fielding, refused to let her sit this event out entirely. He appointed her his assistant, in charge of organizing all the talent, lining up props, creating the lineup, and then supervising the production team so the show and the fete afterwards was a smooth success. In the process, Faye learned she had a talent for coordinating people.