The first point is that if you use tabs, tabs and spaces often get mixed up, and it may be hard to tell one from the other - but when someone else opens the file with a different tab width setting, it's completely messed up. However, the obvious question then is, "why not all tabs?".
The second point is more subtle. Sure, all-tabs vs all-spaces doesn't make a difference for regular indentation of blocks - but there are many other kinds! For example:
while (one_very_long_function_name() &&
another_very_long_function_name())
{
}
Or:
var customer = from c in customers
where ...
select c;
You can't align those with tabs unless your coding style also mandates the precise tab width - and at that point, there are absolutely no benefits in using tabs (well, okay, there is still one - it takes a single Delete/Backspace to unindent the line in Notepad or other primitive text editor). And if you publish code, you'll have to publish tab width as well, since it's not encoded in the file itself.