Your personal experience is not how the rules are written at all. You said two engine airplanes can take off with an engine out. That’s not how it works.
My source is US federal regulations and Boeing Engineering and test and evaluation data demonstrated by Test Pilots and validated by engineering data analysis.
here’s the rules.
Federal regulations
Title 14 CFR 121.189 and 14 CFR 121.617 in additional to Multiple Approved and tested Airline training programs operating under FAR part 121.
Also, General Electric Aircraft Engines must comply with FAR part 31 related to Engine materials, Testing and evaluation.
I said “Can” as in “are capable of”.
Title 14 CFR 121.189 addresses takeoff WEIGHT.
https://www.ecfr.gov/current/title-14/chapter-I/subchapter-G/part-121/subpart-I/section-121.189
Title 14 CFR 121.617 addresses landing conditions at the destination before taking off.
https://www.ecfr.gov/current/title-14/chapter-I/subchapter-G/part-121/subpart-U/section-121.617
Neither addresses the capability to take off on one engine if the other fails.
Don’t try to BS me. Don’t try to BS the forum.
End of discussion.