If Buddha stayed unanswered on this matter, why do his followers preach that soul doesn't exist? Almost every Buddhist I've met sincerely believes in non-existence of self or soul. Especially, the vipassana practitioners say that scanning the body and finding no atman or self in it is proof that self doesn't exist. But what about the practitioner himself who is scanning or performing the vipassana? Doesn't that imply that he himself is the soul?

Also, I found today that Buddha himself stayed unanswered on this matter:


  The Buddha states that it is unwise to be attached to both views of having and perceiving a self and views about not having a self.


So, how can you argue that soul doesn't exist when Buddha himself didn't deny it (or accept it either)? Are there any branches of Buddhism that believes in existence of soul?
Buddhism teaches that everything is 'conditioned', and so there is no independent/eternal self:


  The concept of no-self or anatman or emptiness of self is that it is not possible to identify an independent, inherently existing self; that the self only exists in dependence upon causes and conditions.


You mention "the practitioner himself who is scanning", however 'consciousness' too is seen as conditioned:


  There are four paramatthas; three conditioned, one unconditioned:
  
  
  Material phenomena (rūpa, form)
  Mental factors (the nama-factors sensation, perception and formation)
  Consciousness
  Nibbāna
  




I think this might be a difference between Hinduism and Buddhism:


Hinduism sees liberation/salvation in identifying an eternal self; for example, 'Tat Tvam Asi' or


  You are that, God himself; Meditate this within yourself.

Buddhism sees liberation/salvation in dis-identifying: for example 'Identity view (sakkāya-diṭṭhi)'




According to the Aggi-Vacchagotta Sutta the reason why the Buddha was reluctant to talk about it was that having various (one or more) views about the self did not result in the cessation of dukkha:


  "How is it, Master Gotama, when Master Gotama is asked if he holds the view 'the cosmos is eternal...'... 'after death a Tathagata neither exists nor does not exist: only this is true, anything otherwise is worthless,' he says '...no...' in each case. Seeing what drawback, then, is Master Gotama thus entirely dissociated from each of these ten positions?"
  
  "Vaccha, the position that 'the cosmos is eternal' is a thicket of views, a wilderness of views, a contortion of views, a writhing of views, a fetter of views. It is accompanied by suffering, distress, despair, &amp; fever, and it does not lead to disenchantment, dispassion, cessation; to calm, direct knowledge, full Awakening, Unbinding.


Instead the cessation of dukkha results from the view that everything is impermanent:


  "Does Master Gotama have any position at all?"
  
  "A 'position,' Vaccha, is something that a Tathagata has done away with. What a Tathagata sees is this: 'Such is form, such its origination, such its disappearance; such is feeling, such its origination, such its disappearance; such is perception...such are fabrications...such is consciousness, such its origination, such its disappearance.' Because of this, I say, a Tathagata — with the ending, fading away, cessation, renunciation, &amp; relinquishment of all construings, all excogitations, all I-making &amp; mine-making &amp; obsessions with conceit — is, through lack of clinging/sustenance, released."