GA instructor with student reported an NMAC near BTR airport requiring evasive action to avoid a possible collision. The reporter stated the pilot of the other aircraft appeared to be trying to unsafely follow them until they entered Class C airspace.

Narrative

We were doing chandelles in the north practice area at BTR. We finished with our chandelle maneuver's and we were doing eights on pylons next. We had a small aircraft that we maintained our distance from the traffic. While looking for pylons we had an airplane that ATC told us to avoid. We started doing normal maneuvers (turns; climbs; descents) to get out of his way. Despite my efforts to get out of his way; after a while we figured this aircraft was trying to follow us. This aircraft started following very closely getting to a point where it was unsafe and I felt like he was trying to hit us. It came to a point where if he had a tail number I could read it. It looked like a small aircraft with no tail number. ATC told me to continue inbound for a left downwind for Runway4L. We entered the Charlie airspace. After we reached the smaller circle of the Charlie airspace he dipped off and made a 180 to the north. I was too flustered to continue training so we ended training and landed safely at BTR.