Flight instructor reported violating class B airspace after evading an near midair collision.

Narrative:

My student and I were on a discovery flight; we were on the west side of key biscayne about 1.5 miles west of the island flying south bound at 1;200 ft. MSL. We had been actively searching for traffic; and noticed another aircraft about 500 ft. Lower than our altitude flying south bound as well. However; that aircraft then made a climbing 180 degree turn; then flying directly towards us; my student advised me that the aircraft was getting closer and continued climbing in our direction. I did not have visual of the aircraft and for a moment my student also lost sight of the aircraft. At that moment I then decided to take evasive action and immediately began to climb to stay safe and to evade a near miss or a mid air collision. When my student caught sight of the aircraft again it was flying west bound in a direction that put him right below us. I was able to finally see the aircraft flying west bound about 200 to 300 ft. Below us and continuing to fly away from us. At that moment I leveled off the aircraft to notice that I had violated the mia class B airspace that starts at 1;500 ft. MSL . I'm not sure if we climbed up to 1;700 ft. MSL but I do know that I had climbed to at least 1;600 hft. I immediately descended below the mia B airspace. As I acknowledge that I had violated the B airspace. This was not done on purpose; simply done to maintain the safety of the flight and evade another aircraft.

Original NASA ASRS Text

Title: Flight Instructor reported violating Class B airspace after evading an NMAC.

Narrative: My student and I were on a discovery flight; we were on the west side of Key Biscayne about 1.5 miles west of the island flying south bound at 1;200 ft. MSL. We had been actively searching for traffic; and noticed another aircraft about 500 ft. lower than our altitude flying south bound as well. However; that aircraft then made a climbing 180 degree turn; then flying directly towards us; my student advised me that the aircraft was getting closer and continued climbing in our direction. I did not have visual of the aircraft and for a moment my student also lost sight of the aircraft. At that moment I then decided to take evasive action and immediately began to climb to stay safe and to evade a near miss or a mid air collision. When my student caught sight of the aircraft again it was flying west bound in a direction that put him right below us. I was able to finally see the aircraft flying west bound about 200 to 300 ft. below us and continuing to fly away from us. At that moment I leveled off the aircraft to notice that I had violated the MIA class B airspace that starts at 1;500 ft. MSL . I'm not sure if we climbed up to 1;700 ft. MSL but I do know that I had climbed to at least 1;600 hft. I immediately descended below the MIA B airspace. As I acknowledge that I had violated the B airspace. This was not done on purpose; simply done to maintain the safety of the flight and evade another aircraft.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.

Attributes
ACN	1715199
Time
Date	202001
Local Time Of Day	0601-1200
Place
Locale Reference	MIA.Airport
State Reference	FL
Environment
Flight Conditions	VMC
Light	Daylight
Aircraft 1
Make Model Name	Small Aircraft
Operating Under FAR Part	Part 91
Flight Phase	Cruise
Route In Use	None
Flight Plan	VFR
Aircraft 2
Make Model Name	Any Unknown or Unlisted Aircraft Manufacturer
Person 1
Function	Pilot Flying
Qualification	Flight Crew Instrument Flight Crew Flight Instructor Flight Crew Commercial
Events
Anomaly	Airspace Violation All Types Conflict NMAC Deviation - Procedural Clearance Deviation - Procedural Published Material / Policy
Miss Distance	Vertical 200