In the Doctor Who episode "The Woman Who Fell to Earth" The Doctor removed

several DNA bombs from her companions and reinserted these into the data-gathering coil brought to Earth by Tzim-Sha (Tim Shaw).

The Doctor was not surprised when these found their way back into Tzim-Sha and seemed to understand he was connected to the coil.

Why then,

after Tzim-Sha had detonated the bombs, potentially killing him,

did The Doctor chastise Karl by saying "you had no right to do that!" for kicking him

off the crane? Surely he was as good as dead anyway? Although he appeared to teleport away before we saw him die, The Doctor had previously gone into great detail about the way DNA bombs worked and their deadly potential.

The Doctor's comment to the alien Tim Shaw that it should return home (after having set off the bombs inside itself) would strongly suggest that with the appropriate medical treatment, that the DNA bombs shouldn't be fatal. Since it had no choice but to comply and had stopped actively trying to kill them, that was tantamount to admitting defeat.

Doctor: You got everything transferred to you including five tiny bombs. You had a choice. You did this to yourself.

[ALIEN SCREAMS]

Go home.

In essence, he was killing an enemy that had already surrendered.

It's similar to his reaction to Harriet Jones, British Prime Minister's (*) choice to destroy the Sycorax ship after The Doctor had gotten them to retreat. They'd already lost, in The Doctor's eyes, there was no need to kill them.

One could argue that there's no knowing if pushing Tim Shaw off the crane will result in his death (or at least any more than the DNA bombs will). Presumably, Tim Shaw will return to his planet on some sort of receiving platform, and whether he's on the ground or on the 47th floor of a building would not matter. He was falling as he teleported, but he'd only fallen a few yards or so - when he arrived at home, he'd probably arrive horizontal, but only with the kinetic energy of a very short fall, not a fatal one.

Still, She tells Karl From The Train off, more because at the very least it was a case of kicking Tim Shaw while he was down.

(*) Yes, we know who you are...

Legal right

While the Doctor certainly disapproves of violence on moral grounds, when she said "you had no right to do that!", she may have also meant the legal right.

The Shadow Proclamation enforces interstellar law, including the rules by which technologically advanced societies may interact with primitive societies such as 21st-Century Earth. These strict regulations have been a recurring negotiating tool and/or legal impediment for The Doctor since their first mention in "Rose" (2005).

In "The Woman Who Fell to Earth" (2018), the Doctor may have been relying on this (or similar) interstellar law in her negotiation with the hostile alien. Karl's action, if in violation of legal protocol, may have opened the door to reprisals against Earth.

The Doctor shows a consistent abhorrence of violence which has become more marked over time. One could argue that the first Doctor didn't really show this very strongly, but it becomes a theme over time. KFTT's attack on a defeated foe is well out of bounds for the Doctor's ethos.

In addition, the Doctor does not like to have their plans disrupted, and KFTT's attack disrupted the plan.

She needs to check her Time Lord privilege. Karl was the intended victim of the horrible fate of eternal life on the cusp of death. He was the one with the right and he doesn't have have any idea who the Doctor is.

This is the same Doctor who watched Cassandra explode drowned millions of Racnoss babies and laughs as the Graff explodes from the bomb the Doctor planted on him.

That's all fine for the Time Lord Victorious but the "little people" better not take anything upon themselves.