How the stamp collecting analogy fails

In my recent discussions with atheists in recent times many have responded that 'atheism is not a faith'. They are trying to suggest that atheism doesn't bring with it a kind of 'worldview' that the Christian faith brings with it. They then use the stamp collecting analogy to attempt to demonstrate that a negative or non-belief is not a belief system. Hence the analogy goes, 'not believing in a god as some kind of belief system is like not collecting stamps is a hobby.'
I think it's an interesting move, and it has prompted me to think carefully about this issue, yet I would like to suggest that the stamp collecting analogy fails. I suggest it fails because 'Not collecting stamps is a hobby'. I can, 'not collect' stamps and still be engaged in a hobby. I could collect cloth badges, model railways or pencils, and these are all alternative hobbies. Hence the analogy fails because 'not collecting stamps IS still a hobby'.
But more seriously the analogy fails because it isn't a proper analogy. The analogy is based on a truism and hence it only proves what is assumes. If you change the analogy by inserting other words, you realise this, e.g. 'is like not drinking water is drinking' or 'is like not eating sandwiches is lunch'. 'Hobbies' and 'stamp collecting' (and eating and drinking) are different to 'believing' and 'belief systems'. 'Belief' is a matter of a commitment to certain facts of the world which are often unprovable, whereas stamp collecting is a pastime and can be proved (as can drinking, or eating etc).
Hence, to summarise, Christians believe that there is a God, we can't prove it but we act on 'faith' that it is true. Atheists believe that there is no god, they can't prove it, but they act on 'faith' that it is true. Therefore atheism must be some kind of 'faith' commitment. This is different from stamp collecting because we can 'prove' that stamp collecting exists.
This 'analogy' may appear to offer explanatory power, but in the end, I think, it fails. Can any atheists further explain the stamp collecting analogy, or am I missing something?