what does this mean? - ex bs -

to start things off, me and my ex broke up about a month ago (26 days to be exact) he broke up bc he apparently "needed to focus/work on himself + needed space" our interactions with each other irl and online are completely confusing, unclear, and dumb.
about 5, and 10 days into him breaking up with me he has the audacity to say "I still like you but its complicated" and he says that after we agreed to just be friends.
after that, I start ignoring him in class for a whole week and still am (12 days so far including weekends) I catch him glance or look at me and yesterday at the end of class when we had a few minutes left, I caught him looking at me so I shot him an email saying -please stop looking at me in class -its just odd- and he had the audacity to email a day later saying -i wasn't lmfao. I was looking at the syllabus on the wall. I don't have my contacts on.- I truly think he is lying bc when he was looking at me "supposedly" he wasn't in one place like you would be if you were looking at something. he was walking/passing by while he was "supposedly looking at the syllabus".
then this morning before he sent that email before 1st period, he knows I always walk through the front doors at 7:10 and he (from the corner of my eye) stood there from the side as if he was waiting for me, and I walked to our choir room (the only period I share w/ him) to drop off my track clothes like I do most of the time before 1st period. and when I walked out he was in the hallway facing when you walk out walking/passing by while looking at me. I don't know why he would do that because last week I was walking to do the same thing and once I started walking there he passed by me and looked at me in the eyes (my friends said he was waiting there for 5 minutes and when he saw me coming he started walking)
he's "supposedly" talking/dating another girl from a diff school so idk why he is doing this