I read some where that it was mistake to put your bird cage next to a window overlooking a garden but the article never explained why this is a mistake. Is this true and if so why?

There's many schools of thought on this subject. In my opinion it really depends on where its located in regard to the amount of sunlight that comes through the window, whether there are overhangs on the roof to offer some degree of shade etc. It can also depend on how busy your garden is with wild birds and the size of those birds etc. And it will depend on your bird as well.

For instance, here at my house I have my birds near 3 different windows, 2 that face the east and one that faces south, my east facing windows are somewhat protected because I have a covered front porch and then there is a good overhang on the roof past the porch. So it offeres some protectection from direct sun I have my macaw in front of the large living room window and she does quite well there, she likes to watch the world go by and she also acts as an alarm should someone come into the yard ( like the mail man) This window is protected so large birds like crows and the occasional seagull can't really swoop down and startle them.
Same with my other east facing window it too has the covered porch and what not but it also sits closer to the south cornere so it receives a little more sun light and thus more heat so I usually end up keeping the blind pulled a little longer esepecially in the summer to keep the heat off the window but my cockatoos seem to enjoy that window because they too can see the world go by but are protected from the overhead preditor aspects. I have my little birds in the south facing window and it is not as well protected from the sun because there isn't as much overhang from the roof so I keep a mini blind (or try to ) there to offer a little more protection from the direct sun, and in the summer I also put up a bamboo blind on the outside to keep the hot sun off the window so the birds don't get too hot, That side also has a busier street so I have bushes and what not on that side to kind of block the view a little bit and buffer the noise. I have lots of wild sparrows and finches visit the bird feeder and the pond outside that area of the yard and it doesn't seem to bother my inside birds unless a big crow or something happens to land in the church parking lot across the street, then the alarm calls go off. I think the roof overhang also helps with them feeling somewhat proctected from the overhead prey as well.

Though having them by the windows also makes it more difficult to control the amount of daylight hours they receive so with the birds that really seem to be overly effected by that I cover with dark covers.

Another thing to consider is how drafty are your windows especially in the winter time; cold drafts can really reak havoc on your birds. So if you live in a house that has old single pane windows like I do you should probably make sure that you have storm windows of some type to put on and make sure that they are caulked etc.

It also depends on the persnality of your own bird as well. If they are timid and sudden movement seems to bother them then its probably not a good idea to have them near windows especially if its a really busy area outside, this includes visitors to the back yard such as birds and squirrels etc some birds can be realliy intimidated by any sudden movement be it from the ground or from overhead while other birds even of the same species don't seem to be as effected.

Traffic pattern in your house can also have an effect on your birds so if you place your birds by a window that is in a high traffic pattern in your house that can also be a problem depending on the bird. So there are many aspects that you need to consider about each individual bird and its cage placement. But to just make a blanket statement that birds cages shouldn't be located next to a window in my opinion is incorrect. But that's just my opinion.