Ytdyklly

Suppose that someone initially states that "fossil fuel consumption due to mobile phone usage is similar to that of private transportation, so if you think we should switch to electric/bike to fight climate change, then you should also stop using your mobile".

You call bullshit on that statement, and the debater replies by citing a paper which shows that "worldwide, the fossil fuel consumption of all communication networks, including the Internet is estimated to be about half of the fossil fuel consumption for transportation".

Now the statement is true, but this is not the original statement: it has been unduly extended to make it true. What's the name of this logical fallacy?

Fallacy of division :

A fallacy of division occurs when one reasons logically that something true for the whole must also be true of all or some of its parts.

The OP presents a situation wondering if a logical fallacy has been committed.

The following claim is made:

Fossil fuel consumption due to mobile phone usage is similar to that of private transportation, so if you think we should switch to electric/bike to fight climate change, then you should also stop using your mobile.

The claim is denied without argument.

The person making the claim provides evidence by citing a paper which shows that

worldwide, the fossil fuel consumption of all communication networks, including the Internet is estimated to be about half of the fossil fuel consumption for transportation.

The paper's worth is acknowledged:

Now the statement is true, but this is not the original statement: it has been unduly extended to make it true. What's the name of this logical fallacy?

What needs to be done next is to see how much of the fossil fuel consumption in the report was attributed to mobile phone use.

If the report doesn't have that breakdown one can raise a question about the usefulness of that report. If it does, use that particular number to see if mobile phone use is relevant or not.

Raising a logical fallacy in an argument can backfire. Those listening (the audience) may start siding with the other side as a result. Bo Bennett also warns that if one does start pointing out an opponent's fallacies the opponent may start doing the same. That tactic of calling an opponent's argument logically fallacious may be a distraction or red herring which can itself be logically fallacious.

Here is Bennett's description of red herring:

Attempting to redirect the argument to another issue to which the person doing the redirecting can better respond. While it is similar to the avoiding the issue fallacy, the red herring is a deliberate diversion of attention with the intention of trying to abandon the original argument.

The issue at this point in the argument is whether the data in the report can be used to justify whether one should stop using one's mobile if one wants to fight climate change. Is the associated fossil fuel used large enough? That needs to be addressed and the opponent has taken a risk by providing evidence which can be critically examined.

Bennett, B. "Red Herring" https://www.logicallyfallacious.com/tools/lp/Bo/LogicalFallacies/150/Red-Herring

This sounds like an example of Moving the Goalposts.

"Let me cite this paper which proves my assertion that fossil-fuel-derived energy for cellphone use is equal to the same kind of energy consumption by cars. Look, see right there where it proves that all communications network traffic, including cellphones, uses half the fossil-fuel-derived power that cars use? Goal achieved."

The opponent changed how success was defined in the middle of the discussion.