Is it offensive to stare the speaker's eye?

i think its definately appropriate.
it feels good wen ur speaking to have ppl looking u in the eye,
it shows that theyre listening and it feels really good to
have ppl actually listening to u speak.
it gives a purpose for u to speak.
so its totally appropriate.

but not staring in a creepy way tho.

nope, im in the military and when i talk to anyone especially my higher ups i never leave eye contact with the person thats talking to me or if im talking to them.

no

Staring can be incredibly rude in social situations - it may be read as obstructive and aggressive behaviour.

Using inappropriate gestures in a social situation makes you feel insecure and foolish - other people tend to politely ignore it. (I hope)

Making eye contact (briefly - maybe 1/10th of a second) can say so much. Did you understand the lesson? I agree/disagree. I like/hate you! This is good/bad. etc

Just like smiling, it shows you are happy to be here, and have an inner confidence.

Sit in front of a mirror and practice smiling and making eye contact. Making the right amount of eye contact in any situation is a lot like flirting. If you can get it right (you will make lots of mistakes - but they are helping you to learn), you can only get more confident in yourself.