I don't have to give my blue to mid or my red to the adc

Do people have to leash you?

But I do it anyways. XD

I agree, specifically when you know how to use those buffs to secure leads for your laners. I play Warwick jungle a lot. I use red buff to consecutively gank the same or multiple lanes without need to back for heals. And blue to keep my abilities up, CDR and Mana. Its just, if you know you can put it to good use without giving it to an enemy, then by all means take it. Although, dont be cocky and think "With THIS, I SHALL CARRY" Cause its not how it works. Yes I can easily solo carry with Warwick, but the best games in my opinions for myself, are when i give my laners a lead and feed them a few kills, or bullly their opponents out of lane to get them farm and tower advantage.

You are free to smite your blue, then use it to come mid and depush the enemy malzahar/ziggs with blue on constantly pushing in while I recall out of mana after desperately trying to waveclear . Or look OUR (not mine, OUR) midlane turret falling in pieces. Sincerely, a midlaner struggling against heavy push lanes.

When I jungle I usually smite buffs from my team because I need the exp.

No, you don't have to, but it's beneficial for you to. You, as the jungler, have more free time available to back and go into whichever side of the jungle you need to. In lane, blue and red will (generally) have more use, letting your laners get some free poke or to harass without that much worry. As for you, it'll generally go towards clearing your camp, maybe counter jungling a little, and if you're really good, setting up some good ganks to push your laners ahead. If you can't do a combination of all of these efficiently, then it'll be best left to your laners. But that's just my opinion.

Idk why other ADCs want the buff so bad. In my eyes, the time spent walking to collect the buff would be better used farming or defending my tower, but if it’s offered I accept it.