Next one then:

Which path should we choose? Option A: a lot of minor enemies. Option B: Less enemies but we will have to make a frontal attack on an enemy that should definitely be flanked. What to do, what to do? Sadly, my repairing abilities are limited so we cannot choose option A. We will have to face this huge enemy in option B. But don't worry my troops I won't let him destroy you. I'll create a clever distraction and you will take him down him before he realize that it was just a decoy.

Warcraft 3
Heroes of Might and Magic 2: Price of Loyalty
Red Alert series?

You can't repair buildings in HOMAM2, so I bet that one's not it.

Honestly, I'm not even sure what genre to go for, this is a very vague description - at first I thought it's some kind of a tower defense or Plants vs Zombies type of a game, but with the option b) I'm not sure at all what kind of a game to think of - is the 'path' level selection? In that case it might be something like Orcs Must Die and so on, if not, maybe it's an RTS?

No good answer so far but let me emphasis that "the path selection" is literal - like turning left and facing a lot of weaker enemies or turning right and - once again very literal - launching a frontal attack on enemy that ideally should be flanked. But he can be tricked by a decoy so it's better to take that path.

Sounds like the entire plot of Lord of the Rings to me...

heh, heh that was nice :) But I don't think I've played any LotR game in my life

Maybe another hint? ;)

OK, here it goes:

Taking option B was a very good decision. We didn't lose a single unit!. But now we have to prepare for a difficult fight. Our enemy tries to destroy a bridge and must cross it! Let's go, let's go! I'll be calling an airstrike and smokescreen to cover you from enemy. We must cross the bridge before it collapses!

No... I didn't expect that it would be so hard. I'll try once more and if not I'll give a hint that will practically reveal everything.

OK, so we've rescued this professor lady. What was she doing in the middle of this hell? How did she survive that long? I've no idea but I'll have to think about it later. Now I should focus on how to utilize this protection device that she offered us. It looks sweet I think we may save a lot repairs by using it efficiently. I won't be afraid of losing my weaker units so easily anymore!

Sounds like something from the C&C series - the original Red Alert?
edit - someone already guessed Red Alert series, looking back... hmmm...

Yeah, it's not C&C, it'm much newer game. Remember about branching path (very, very literal). In standard RTS games you can move your troops wherever you like...

Worms?

Oh wait, no. That doesn't make sense with the professor lady info.

I have a vague feeling it might be Starcraft 2. I could tell for certain if I got to actually play it.

Nope, not this game (I've never played it). And once again: in standard RTS game you don't have well defined branching paths to choose, you can move (almost) wherever you wish.

And... this game is on GOG ;)