"... if a word is demanded, "which" is not correct. The proper choice isn't listed; it's that".
Parla, I'm afraid this isn't true, although US style seems to favour 'that' in a way which sounds strange to these British ears.
'Which' can be used in both restrictive and non-restrictive relative clauses, whereas 'that' can only be used in restrictive relative clauses.
All the reasons he gave for wanting to change his job were quite unreasonable.
All the reasons which he gave for wanting to change his job were quite unreasonable. (preferred in British English)
All the reasons that he gave for wanting to change his job were quite unreasonable. (preferred in US English)
All the above are acceptable.
See "that" in the Word Reference dictionary - sorry, I couldn't post the link.