Why are downloads destructive in the Star Trek universe?

Downloads are not in and of themselves dangerous or destructive. In the first episode that you asked about, "Twisted"

B'Elanna reports that 20 million gigaquads of information was uploaded to their computers, while their computer database was copied

nothing was deleted information was added.

In the case of the episode "Message in a Bottle" the Doctors program was transferred from the mobile emitter to the transceiver array for transmission to the alpha quadrant. The entire EMH Program had to be transferred in order for it to function either in the emitter or as a subspace message. Voyager's computer was not capable of holding the original program and making an additional copy because of the size of the EMH program, The Doctor's entire program used 50 million gigaquads. That's why the Doctor was not available in sick bay and Paris was trying to hold down the fort.

"Message in a bottle" is bad example for the question, because hologram is very specific type of data/program. This was noted in question here:

Why would Professor Moriarty "cease to exist" if he tried to exit the holodeck via the arch?

As for the destructiveness of the copy/download I think you read too much into things.

Every time I remember when the download is "destructive" involves holographic data - i.e DS9 "Our man Bashir". Also, at least in Starfleet, the drive is to log everything.

Data destruction clashes with imperative to gain knowledge, so I believe you're asking about something you imagined. Not trying to be condescending here, just stating facts as I see it, so sorry if I offended anyone - not my intention.

So the only answer that would fit RL and in Universe is:

Star Trek computers work totally diffrent from how computers work now.

Sadly the authors do not provide insight on how isolinear computer technology works in detail, so it is hard to understand how copying and storing data in the Star Trek universe actually works.

From a real world perspective it is complete nonsense as any data stored somewhere is never erased by copying it. You have to either turn off the power for volatile memory or even actively erase the data from non-volatile memory.

Thus the only conclusion can be that Star Trek computers work in a totally diffrent way than our current computers.

That might actually not be so far fetched since we are approaching the physical boundaries of what you can achieve by CMOS technology. Currently Intel is developing 10nm technology - silicon atoms are 0.11 nm wide. So the gate length approaches atom diameters. It is expected that if the gate length is about halved again, quantum tunneling will be a non-neglectable phenomenon.

So by the 24th century, computing technology might be something totally different from what it is today simply because our current progress is reaching its physical limits.

On the other hand, current verly large storage systems can handle and store data in the range of Peta to Exo-Bytes. A human body has about 10^28 atoms. If beaming means storing all that information within the computers of the transporters, it would need some incredible storage and processing power on a level much much smaller than an atom... otherwise it would at least as many atoms to "store" the human information in another form - in that case a prefect 1:1 clone.

Even if holograms would be a lot less complex due to algorithms etc., it would still mean a tremendous amount of calculation power and memory to render and store holograms of that detail that they are indistinguishable from actual human beings.

This answer is pure conjecture:

Starfleet computers could have safeguards in which they will not give up a piece of data without destroying it in the process, to prevent files from being read or modified without the crew's knowledge.

This could be accomplished with encryption. When created, a file would be encrypted with key-pair encryption and the computer would immediately destroy the public key and keep the private key only until the file is read. Then it would destroy the private key and probably the data itself as the data was read.

Copying then would be a procedure where you read a file, save two new copies with new keys, and destroy the original. (Or save one new copy and transmit the other)

Opening a file then would read the file to active memory, destroying the original, and saving a copy under a new key.

You could probably even use this method along with user credentials to make it impossible to hide who last accessed a file.

That would explain why just downloading would be destructive.

My guess would be that computers in the Star Trek universe are based on quantum-mechanical technology, and data is stored as a pattern of quantum states. It is well-known in the physics community that quantum states -cannot- be exactly replicated; this is known as the "No-Cloning Theorem". I would speculate that part of the process of reading stored data involves 'quantum teleportation' of the relevant data to a holding area where a destructible digital copy of the data is fabricated, after which the original data is 'teleported' back. The same process, applied between ships, would account for the phrase "copied and downloaded" (though I would phrase it as "downloaded and copied" myself).