Fathom and Phantom 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 suggests what word you may want to save time, but quite often, its suggestions couldn’t be more off base and produces humorous results.
Fathom is a noun. It’s a nautical depth of measurement equalling six feet. It also can mean to measure depth via a sounding device.
Fathom is also a verb. It means to think or imagine a concept. This is the usage I hear most often.
Phantom is a noun. It means a supernatural being or an illusion, something sensed but not visible, or that really exists.
Phantom can also be an adjective, to describe something that no longer exists. When a person has an arm or leg removed, sometimes they sense that part is still there: this sensation is called phantom limb.
The following story uses both words correctly:
The Phantom of the Opera is an enduring romantic tale from 19th century France. In it, Christine, the heroine, can’t fathom why a mysterious stranger, her angel of music, would help her transform from a common chorus girl into the star of the opera. But once her dreams start to come true, she learns what the Phantom wants in return.