There is not always an unambiguous conversion from one TZ to another.
DST will always give you an ambiguous localized time. If you take input in local time, and it's in the repeating DST window (01:00<=t<02:00 for spring in USA).
Don't get me started on start of day or start of week in multi-TZ /culture environments. If you think times are bad, look at calendars.