Does the revolution of the earth bother us in our day-to-day activities? If yes, how? If not, then why do we teach and study these thing?
Isn't it right that we have to study only those things that are relevant for our survival?
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If you interact with people anywhere else on the planet, knowing the basic configuration of the earth and the sun makes it much easier to understand time zones, different seasons in the northern and southern hemisphere, and so on. If you care at all about weather and live outside the tropics, it's a helpful organizing principle to understand the progression of seasons. It lets you realize that a day is the same duration whether or not it's summer or winter.
You could just memorize hundreds of isolated facts (and you probably will anyway), but why not learn an organizing principle--of how the thing actually works--in order to make sense of it?
More generally, one may want to learn things for physically practical reasons, or for socially practical reasons, or for personal development even if directly impractical. Basically all of what is taught, as far as I am aware, falls into one of these categories, or at least attempts to. Poor teaching may fail to achieve any of these ends (or may succeed but without you noticing that there was something practical in there), but that's a different issue. One may also research or investigate things not known to be practical, but that's another different issue.
I'm going to answer the title. The model of the earth rotating around the sun is a much simpler and more explanatory model than the universe revolving around the earth. You could well build a model with the sun spinning around the earth along with everything else, but you'd find the model gets very complicated very quickly and it becomes more difficult to use the model to change the world around us, hence its abandonment and the Copernican revolution.
Your second question depends upon what you care about. If you care about space travel, satellites, weather forecasts and star gazing; it's very important. If you care to learn the mind of the creator, also important. If you care about acquiring more knowledge for its own sake, it's important. If you care about none of these things (or things similar to these) and you don't interact with people who do, then it has no impact on you and you have no need to care.
Does it impact upon our survival? As mentioned already, space travel, weather forecasting, satellites, space science, these are all shaping our lives at the moment. And if you think we should only study things that impact on our survival, then we must care about the earth going around the sun.
Revolution of the Sun around the Earth - and/or other way around - bothers us in as much as it causes a sequence of intervals of light and dark, cold and warm. If it didn't bother us we'd have no need for artificial illumination and heating.
But does it matter which actually moves and which is static, if any? Well yes. If you're a professional mechanical planetarium builder, you'd better stick to geocentric worldview during working hours, since you want your audience to stay put while you rotate your sky projections around them. Poetry is another every day activity, where Sun goes around the Earth regularly. On the other hand, if you want to send a rocket to mars, you'd better off considering the Sun to be in the center and planets go around it while also rotating around their axes.
No, we don't have to study only things relevant to our survival. We don't have to study at all: behold the fowls of the air: for they study not, neither do they teach, nor write encyclopedia; yet they survive OK. Are we not much better than them?
On the other hand studying often provides mankind some advantage or another compared to other beasts. And as rraallvv points out we don't always know upfront which of our studies will end up providing such an advantage. Hence it is clever to try to figure out as much as possible.
It's impossible to know every consequence of our research beforehand and our motivation is just that we don't know.
All we can do is find out as much as we can, and then test and figure out later.
Luckily enough it has worked for us most of the time. Think of atomic bombs, for instance.
So, whether Earth revolves around the Sun or if it's the other way around, it's not vital for us as individuals or as a group in our day-to-day life, but we don't know for certain how something could affects us before trying to find out about it.
From a philosophical point of view one might ask whether that is a self-destructive behaviour, because humanity could face extinction trying to find out about it by experimentation :)