Put a garden variety Swede next to a native Australian: How much trouble would you really have defining the differences?
But this is exactly the point - people think they can easily see the difference, but it turns out that when you look at the actual genetics, what people think often turns out to be wrong. For example, take two African Americans (often considered by many people to be a race) and a random white American. It's not particularly unlikely that each of the black people will be genetically more closely related to the white one than they are to each other. So how could African American possibly be a race? The answer is that it isn't - basing the idea of race purely on looks just doesn't work.
Or another example. Take your native Australian and put him next to a native South American. They may well look very similar. But the South American is probably much more closely related to an extremely white Russian who you'd probably group with the Swede, since that's where the main migrations that colonised America originated. Once again, the concept of race based on looks falls apart.
It gets even worse if you look at a group like "Latino", which is purely a cultural and lingual grouping and has nothing to do with genetics at all, but is still often referred to as a race.
Of course, some people do take this way too far in a silly PC way to somehow imply that there are no differences between us at all. Obviously that's not true. But what is true is that traditional views of race based almost solely on a couple of visual features, skin colour and facial structure, are at best horribly flawed, and often are just complete nonsense.
When you look at it in a scientific manner, it turns out that while you obviously can group people by how closely related they are, those groups have very little in common with how the term "race" has been used traditionally, and is really of very little use at all. It's not that race doesn't exist at all, it's simply that how people use it is usually very different from how they
think they're using it, and that's different again from how it actually should be used.