Hmm. Speaking as both a dancer and a dance teacher, there will always be some that have to work so much harder to get half as good as others (and similarly, some people who will be at a natural advantage). But that doesn't mean that you can still become a decent dancer - it just takes practice and good training. It is definately NOT 'just suited for certain people'
Some teachers will mentally dismiss dance students that look like they have 'learning difficulties' but in my opinion this is because they don't have the patience to work with the basics. You gotta start with a good foundation, you know?
For example, most great dancers are blessed with an excellent sense of rhythm/musicology - most 'normal' people have varying levels of this (very few are totally tone/rhythm deaf). So what you teacher should do at this point is just work on your musicology - start by knowing how to pick out the rhythms, then doing simple choreography that basically goes beat for beat (eg stepping). As you get better and have to concentrate less on the music, you can learn to start layering and mixing up steps (eg choreography that accents/travels on off beats rather than on the beat). The trick is ALWAYS to start off simple. Then work with that will you're 100% comfortable with it - then you go up a notch on the challenge meter, work with that till you're 100% comfortable, go up another notch etc etc.
Musicology aside some people just have issues picking up steps within a short period of time. There are more or less two types of choreography learners - 'Audio Digital' and 'Kinesthetic". The former are those nutty people who can watch something once and do it perfectly. The latter has to do it over and over again and ingrain the choreography into their body memory before they can perform it as comfortably.
That being said, even a kinesthetic learner (I'm kinesthetic too btw
) can improve their pickup speed by being challenged over time, and 'raising their bar' so to speak. This is going to sound totally stupid but I'm going to relate it to maths - you start off with 'simple' algorithms which seem hard. But then when you start learning harder ones (and being pushed to get the right answer fast) those earlier ones seem easy, yes?
Also, the more experience you have the easier it will be for you - of course someone who has been doing classes for a longer time than you will (at the start, anyway) be better at picking up choreography because they've had more experience at that sort of thing. We all start with nothing
As for style, this is something that will come with time. I have always felt that a dancer will ONLY really put their style in when they are comfortable with a step - so if it just means that you're not comfortable with it yet, don't worry! You soon will be
Keep working hard and just let it develop naturally - it won't happen overnight but it does happen