You should check the Underwater Combat rules - there's loads of restrictions for creatures lacking a swim speed.

Something that people don't understand about speeds (other than maybe flying) is that just because you can do something doesn't mean you get that speed.

Burrowing is probably the best example of this. "X creature LIVES underground in burrows it dug itself! Why doesn't it have a burrow speed?!" Can it burrow at least a foot per second through a tunnel it's inside of with relative ease? No? Cool, then there's no point in giving it a burrowing speed.

As far as swimming goes, there are several reasons to not just hand out a swim speed. First and foremost is that creatures already can typically swim at half their movement speed regardless. In the case of tigers, yes, they are good at swimming for big cats, but they can't move more than half their land speed in the water, so why make a special note of it.

Second is that swimming speed doesn't just grant the ability to swim (which it doesn't even do). Having a swim speed makes you proficient in underwater combat. Weapon attacks (i.e. not spell attacks) normally have disadvantage underwater unless they are one of a select few types of weapons. The exceptions to this rule are creatures with a swim speed. Can the tiger bite and claw just as well underwater as they can on land? I don't think so.

If you've seen a panther climb a tree, you would probably agree that they deserve a climbing speed. Add that to the fact that climbing is normally done in short bursts and (as far as I know) there is nothing special granted with a climbing speed as there is with swimming. You still need to make checks RAW. All you get is a speed that isn't halved while climbing. Other features like spider climb allow for you to avoid checks or climb where you otherwise would be unable to do so.

Tigers are poor climbers though unlike leopards (panthers). It's the main way leopards avoid tiger predation in Asia and lion predation in Africa. They can swim very well but don't really have a need to climb when their main prey is large ungulates.

hbdjhdz

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How come they don't have proficiency in Athletics? Aren't they like the biggest and strongest of the big cats?

I'm a beastmaster ranger weretiger tiger tabaxi with a pet tiger.

(Tigers are my favorite animal.) 

omg i love the tiger so much im a druid so FOR SURE

CLICK HERE TO SEE THE: Summoning Orb (Tiger)

a tiger should also have something like sneak attack. Tigers sneak up, attack by surprise and from behind their prey. I think a +1d6 for surprise would be fair.