I'm wondering exactly how much we're really damaging our planet through pollution and waste, as opposed to what the media tells us...
The trouble is there are many separate issues that tend to get conflated in these sort of discussions. Firstly, we're not damaging the actual planet in the slightest. The Earth is a damn great lump of rock and the worst humans, or any life for that matter, can do barely amounts to messing up its makeup. Even having flying rocks from space smack into it does little more than add the odd dent here and there.
Assuming you actually mean to talk about life on the planet rather than the planet itself, there are still a number of separate issues. Wiping out life itself really isn't an issue. The flying space rocks mentioned above did far better than we could manage, and even they never managed to kill everything. Life is pretty damn resilient.
However, while life in general is fairly tough, specific forms of life may not be. Killing everything may not be feasible, but killing a large proportion of certain kinds of life is. For examople, the K/T impact is famous for wiping out the dinosaurs, but left mammals and birds relatively untouched. Humans have the same sort of effect - we actively promote the welfare of some animals like cows, kittens and the like, we indirectly help others like rats, we purposely wipe others out, like tigers and rhinos, and we accidentally kill others by doing things like cutting down trees. We're not about to wipe the Earth clean of life, but we can do some pretty hefty readjustment of ecosystems. Whether you count that as damage or simply natural evolution is a matter of taste.
In the end, what you need to remember is that we look at things from a human perspective. Humans have evolved under certain conditions. Even more importantly, human civilisation has developed under very specific conditions, and modern civilisation even more so. The fact that climate and ecosystems change naturally is irrelevant, no matter how natural or unnatural it might be, we're not currently capable of dealing with a world with 60m higher sea levels and double the oxygen content in the atmosphere, for example. That may have been great for dinosaurs, but not for us.
The problem with global warming, pollution, fish stocks and what have you is not that the world is going to end, or even that the world is going to end for humans. The problem is that our current civilisation is based on having the sea stay put, having drinkable water in particular places, having food swimming around the place, and so on. If those things change, whether through moving or simply being used up, and whether due to entirely natural causes or through our own faults, we're going to have issues.
And the more people there are, the bigger those problems will be. A 1m change in sea level 2000 years ago may have got a few villages a bit damp. A 1m change in sea level now could mean millions of homes under water, simply because there are millions more homes than there used to be.
As for the specifics of how much we're damaging things compared to what is reported, that depends entirely on what reports you've been reading. Personally, I've never even heard of any "Great Pacific Garbage Patch", and I doubt it exists. On the other hand, holes in the ozone layer certainly do exist, as do things like acid rain and smog. Global warming itself is pretty certain, although the exact effects are still up for debate.