Yeah idk why Americans say it nitch... there is no T in it lol
Americans (and other English speakers; there’s not much difference between most English dialects in this case) don’t say it as “nitch”, they say it as “nich”, precisely rhyming with “lich”, “rich”, or “which”. The sound here is a glottal stop, not a “t”. It’s just that words ending in -tch like hitch, pitch, witch, glitch, itch, etc. are pronounced in approximately the same way, because often the “t” sound in those words is often mostly or entirely replaced by the glottal stop.
As Wikipedia puts it: “Standard English inserts a glottal stop before a tautosyllabic voiceless stop, e.g. sto’p, tha’t, kno’ck, wa’tch, also lea’p, soa’k, hel’p, pin’ch.”
And also: “In many accents of English, voiceless stops [...] are glottalized. This may be heard either as a glottal stop preceding the oral closure ("pre-glottalization" or "glottal reinforcement") or as a substitution of the glottal stop [ʔ] for the oral stop (glottal replacement). Pre-glottalization normally occurs in British and American English when the voiceless consonant phoneme is followed by another consonant or when the consonant is in final position. Thus football and catching are often pronounced [ˈfʊʔtbɔːl] and [ˈkæʔtʃɪŋ], respectively. Glottal replacement often happens in cases such as those just given, so that football is frequently pronounced [ˈfʊʔbɔːl].”
I suppose you might sometimes get the reverse situation, where people insert an explicit “t” sound into the way they say “niche”, “lich”, “rich”, or “which”, just to make it consistent with similarly pronounced words that do have a t in them. This is non-standard though, and I don’t think it’s too common.