Why does the Rogue not have proficiency with a whip by default? It has the finesse property, so i assume i should be able to use my Dex modifier with it.

the only ways i can get proficiency with it is by multiclassing into Fighter, or by multiclassing into Kensei Monk and picking a Whip as a Kensei Weapon. 

Even if a whip is not a very effective weapon on its own it might be fun. There is also the symbiotic whip which is pretty cool, I'd like the flavor of a Rogue with it bonded to him and extending from his wrist.

Someone once mentioned that whips are just in the game so that enemies can wield them and it made a lot of sense to me. They were not well supported in 4e either, even though all they had to do was add the flail tag to them. WotC just doesn't seem to want PCs to use whips.

Now if you use Tasha's character origin options, you can swap out any racial proficiencies you get for others. So I believe a dwarf could trade battleaxe proficiency for a whip, for example.

I believe the feat you are looking for is below. You can take Whip as such a weapon with it being Martial type.

https://www.dndbeyond.com/feats/weapon-master

I should also mention that you have a lot more multiclassing options than fighter and kensei monk:

1. Barbarian
2. Paladin
3. Ranger
4. Any cleric domain that gets martial weapons (war, tempest, etc)
5. Valor bard
6. Bladesinger wizard

5e scorpion whip/blade... makes it all worth while