Why is Data so surprised that he's mortal?

Question

In "Time's Arrow," the discovery of Data's head in a cave is evidence that Data is to die at some point. During a conversation with Geordi in Ten Forward, Data tells him that such a revelation doesn't bother him in the slightest; outliving all of his friends would only reinforce the notion that he is artificial. Finally, he concludes that the finding of his head shows that he's mortal.

However, unless Data, for some strange reason, thought his head popping off would result from "android old age," then I'm not sure why this discovery would make him question his "immortality." After all, Data could have died previously by many different methods: Q could've destroyed him, the ship could've exploded, a phaser set to vaporize, etc. Data knew that he was mortal in this sense. So, I don't understand what his point to Geordi is.

Answer 1

Knowledge of mortality and actually being slapped in the face with the fact of your own death are two separate things. Data knew in the abstract that he could be destroyed; however, he had never actively thought about death.

His point to Geordi was simply that, barring some accident, he can't die a natural death and, before finding the head, there was no guarantee that an accident would occur. There is also the possibility that Data was attempting to comfort Geordi, kind of a "do not mourn for me friends for I am happy where I have gone".

Answer 2

Data explains this in the episode

In 'Time's Arrow Pt 1', Data says:

LAFORGE: So, do you want to talk about it?

DATA: Are you referring to the foreknowledge of my death?

LAFORGE: Yeah.

DATA: I have no particular desire to discuss the matter. Do you need to talk about it?

LAFORGE: Yeah.

DATA: Why?

LAFORGE: Data, this has got to bother you a little.

DATA: On the contrary. I find it rather comforting.

LAFORGE: Comforting?

DATA: I have often wondered about my own mortality as I have seen others around me age. Until now it has been theoretically possible that I would live an unlimited period of time. And although some might find this attractive, to me it only reinforces the fact that I am artificial.

He is making the point here that, although he is susceptible to other forms of death as mentioned in the question, it is theoretically possible for Data to live forever. Some people simply die of old age - as long as Data's systems are kept running smoothly, this will not happen to him (unless he has a 'death' system installed in his programming like in Juliana Tainer). Consequently, it was possible he could continue living indefinitely.