(NOTE: Here's a really long explanation!)
-As you should know, there are multiple G-Man entities across Half-Life. Just to point some out, there was one in the window talking to a scientist, one on a ledge where the first houndeyes were, and the ending (obviously). However, there can only be ONE G-Man, so if you kill one, then how would they stop G-Man from showing up again? Well, maybe an env_global or something, but then, how would the ending work then? To recall the ending, (NOTE: Obviously, spoiler for those who haven't played Half-Life 1) G-Man takes away all of your belongings except the HEV suit, claiming they weren't your property (besides the HEV suit). Then, he would offer you a job. So, if you killed the G-Man earlier in the game, who would take away your weapons? Who would offer you the job? See, killing G-Man would ruin the plot since the ending would be messed up, and then G-Man coming back in the beginning of HL2 talking about how you were in statis and blah blah blah wouldn't make sense if you killed him in HL1 because if he was killed, how would he come back? Plus, if you never saw the ending of HL1, then how in the world would you understand the intro of HL2? You wouldn't know what he was referring to as "the job" or "putting you into statis". (NOTE: I didn't actually play HL2, I just played the demo on my bro's comp) So, to prevent that, Valve just made him invincible.
That was really long.