In what case you would say "I am seeing" instead of "I see"?
To summarise other people's answers, there are three uses of "I am seeing":
It should usually be for a process in progress.
Should you send a quick message from a movie theater during the projection of a film, you would type:
(and not "I see...")
The expression "to see someone" (meet regularly as a boyfriend or girlfriend) is more often used as:
“I see” describes the present.
To describe something that is ongoing you use the word “be” + a word with the ending “–ing”. As in:
I am seeing, feeling, dancing...
I guess 'to see' is something you could/should be doing with your eyes.
I see what you are doing there. I see the doctor every day
'Seeing' something/body should be for the action itself.
I'm seeing what you did there. I'm seeing the doctor everyday since my infection started.
"To see" is what is considered a punctual achievement verb; a verb that happens instantaneously. Other examples of achievement verbs are: catch, faint, hit, kick, recognize etc.
Many of these verbs cannot take the progressive form to describe an action that is happening at the moment of speaking. For example, we can't say,
"He is seeing the movie." or, "I am seeing myself in the mirror."
Rather, in these cases, we use the simple present tense:
"I see you!" "Do you see that crazy guy over there?"
Furthermore, using achievement verbs in the progressive tense means that the action is repeated (iterative):
"Why is he kicking the door?" or, "I'm catching butterflies!"
Now, onto the present progressive, "I'm seeing..." As stated earlier, this can be used to express