Why do we say 'chairman' for men and 'chairperson' for women? Why don't we use 'chairperson' for both?
It's a neutral word a single word can used for both.
Also, why do we use 'man-made' environment? Why don't we use 'human-made' instead?
'Chairman,' 'chairwoman,' and 'chairperson' are all acceptable and all in common use. Chairperson is not restricted to use with women, and the AP Stylebook (2013) recommends against it. It instead suggests 'Chairman' or 'Chairwoman' in all cases, except where 'Chairperson' is a person's official title.
Neither Merriam-Webster nor the AP Stylebook accept 'human-made' as an alternative to 'man-made,' but 'man-made' does not suffer from the same gendering problem as 'chairman' and 'chairwoman.' 'Man' originally meant just any person, and though the use of man alone to mean just any person is obsolete, the meaning persists in a number of words. The OED gives two examples that describe both Adam and Eve as men.
C1175 (OE) Homily (Bodl. 343) in S. Irvine Old Eng. Homilies (1993) 138 He [sc. the Devil] þam ereste men Adam and Euam..forcostode and biswaac.
1597 Bp. J. King Lect. Ionas xxxvi. 481 The Lord had but one paire of men in paradise.
For that reason I personally don't have a problem using 'man-made,' but one could use 'artificial,' 'synthetic,' or 'simulated' depending on the context to avoid the term.