One human is condemned if he kills another human, but if the same human killed an animal it is not a big deal and you won't even receive jail time (atleast in my country). How did we decided that one is bad since both human and animal are living creatures? Afterall, other species also kill individuals of their own kinds in the natural course of competing with each other. Is there philosopher who wrote about this or any resources etc?
Firstly, what is punishable by law and what is moral are two very different things, and it would be a mistake to conflate the two. While someone may not go to jail for killing an animal, this does not thereby guarantee that it is morally permissible to kill an animal. Going in the other direction, it may be illegal to consume certain substances (for instance), but this does not mean that it is morally impermissible to consume them - the law could just be confused on this mark. Similarly, what is natural is not a good guide to what is moral. Arguably things like rape, murder, war, famine etc. are just as 'natural' as a non-human predator killing its prey for food, but we wouldn't want to say that those things are moral.
Secondly, the answer to the question "is it morally permissible to kill animals?" will depend on the kind of normative ethical theory that one adopts (or, which normative ethical theory is correct). A normative ethical theory is a collection of principles that tell us which actions are permissible, which are impermissible, and which are obligatory. The most common kinds of normative ethical theory are consequentialism, deontology, and virtue-based.
Consequentialism holds that we have an obligation to maximize utility, where we can fill out the notion of utility in a variety of non-equivalent ways (e.g. as pleasure, happiness, flourishing etc.). So, a consequentialist will say that it is permissible to kill the animal so long as you ensure that doing so will maximize utility. Similarly if killing the animal won't maximize utility, then it is impermissible to kill it. See here for more.
Deontological theories hold that what is (im)permissible is a matter of the kinds of duties and obligations we have to each other. So if I have an obligation (say) not to harm living creatures, then it would be impermissible to kill an animal, because in doing so I wouldn't be observing my obligation not to do so. Similarly, where I have an obligation not to harm living things, living things have a right to not be harmed by me. By killing the animal I would be violating that right. Here's more on deontology.
Finally, lots of ethicists have written on animal ethics - whether they are part of the moral community, and if so, what kinds of moral rights do they have? Peter Singer is probably the most well-known philosopher that works on these problems, and his writing is accessible. Here is some of his work.