The pronunciation of Greek letters by scientists isn't very different from the pronunciation of the Greek letters in the respective countries: American scientists pronounce them pretty much the same way the general American population does, and so on.
So your question is actually about why the English pronunciation of Greek letters, and the answer is that it is based on (but not always actually very close to) the reconstruction of the Classical Greek pronunciation by Erasmus in 1528 and by John Cheke and Thomas Smith around 1540, which were adopted in schools. This pronunciation underwent some change along with the rest of English during the Great Vowel Shift, and a re-reconstruction in the mid-19th century brought it back in line (incompletely) with Ancient Greek. The Wikipedia page on Pronunciation of Ancient Greek in teaching has more details.
For sake of completeness, here's a (very incomplete) table showing the pronunciation in American English, British English, Ancient Greek, and Modern Greek. I've rearranged the alphabet to put sort-of rhyming letters together, but all letters are there.
[Disclaimer: Many of the entries may be terribly wrong. The American and British IPA entries are based on the article English pronunciation of Greek letters, the "pseudo-phonetic spellings" are from here and here. The Classical and Modern Greek pronunciation columns I made up, partly from Swedish Wikipedia, partly from piecing together each letter's pronunciation in this table, partly from here for Modern Greek, and partly on my own — and I don't actually know IPA.]
[Edit: This table has now been edited to correct the IPA and source Classical Greek pronunciations from the English Wikipedia.]
Name American English British English Classical Modern Greek
Greek Greek name
Alpha /ˈælfə/ AL fuh /ˈælfə/ AL fuh [aːlpʰa] [aːlfa] ἄλφα
Beta /ˈbeɪtə/ (BAY tuh) /ˈbiːtə/ (BEE tuh) [bɛːta] [vita] βῆτα
Zeta /ˈzeɪtə/ (ZAY tuh) /ˈziːtə/ (ZEE tuh) [zɛːta] [zita] ζῆτα
Eta /ˈeɪtə/ (AY tuh) /ˈiːtə/ (EE tuh) [ɛːta] [ita] ἦτα
Theta /ˈθeɪtə/ (THAY tuh) /ˈθiːtə/ (THEE tuh) [tʰɛːta] [θita] θῆτα
Pi /ˈpaɪ/ (PIE) /ˈpaɪ/ (PIE) [peɪ],[piː] [pi] πεῖ
Phi /ˈfaɪ/, /ˈfiː/ /ˈfaɪ/, /ˈfiː/ [feɪ],[fiː] [fi] φεῖ
(FIE, FEE) (FIE, FEE)
Chi /ˈkaɪ/ (KIGH, KEE) /ˈkaɪ/ (KIGH, KEE) [kʰeɪ], [çi] χεῖ
Psi /ˈsaɪ/,/ˈpsaɪ/,/ˈsiː/ /ˈsaɪ/,/ˈpsaɪ/,/ˈsiː/ [pseɪ], [psi] ψεῖ
(SIGH, PSIGH, PSEE) (SIGH, PSIGH, PSEE) [psiː]
Xi /ˈzaɪ/, /ˈksaɪ/ /ˈzaɪ/, /ˈksaɪ/ (ZIGH, [kseɪ], [ksi] χεῖ
(ZIGH, KS EYE, KSEE) KS EYE, KSEE) [ksiː]
Gamma /ˈɡæmə/ (GAM uh) /ˈɡæmə/ (GAM uh) [gamma] [ɣamma] γάμμα
Delta /ˈdɛltə/ (DELL tuh) /ˈdɛltə/ (DELL tuh) [delta] [ðelta] δέλτα
Epsilon /ˈɛpsɨlɒn/ /ˈɛpsɨlɒn/ (EP sil on), [e psilon] [e psilon] ἒ ψιλόν
(EP suh lon) /ɛpˈsaɪlən/ (ep SIGH lun)
Upsilon /ˈʌpsɨlɒn/ /ˈʊpsɨlɒn/,/juːpˈsaɪlən/ [y psilon] [i psilon] ὖ ψιλόν
(UP suh lon) (OOP sil on, YOOP sil on)
Omicron /ˈɒmɨkrɒn/ /ˈɒmɨkrɒn/, /ˈoʊmɨkrɒn/ [omikron] ὂ μικρόν
(AH mih cron, /ˈoʊmaɪkrɒn/ (OM ih cron
OH mih cron) OH my cron)
Omega /oʊˈmeɪɡə/ /oʊˈmeɪɡə/, /ˈoʊmɨɡə/ [o'meɣa] ὦ μέγα
(oh MAY guh) (oh MAY guh, OH mee guh,
OH meg uh)
Iota /aɪˈoʊtə/ /aɪˈoʊtə/ (eye OH tuh) ['jota] ἰῶτα
(eye OH tuh)
Mu /ˈmjuː/, /ˈmuː/ /ˈmjuː/ (MYOO) [mŷː] [mi] μῦ
Nu /ˈnuː/ (NOO) /ˈnjuː/, /ˈnuː/ [nŷː] [ni] νῦ (NYOO, NOO)
Kappa /ˈkæpə/ (CAP uh) /ˈkæpə/ (CAP uh) ['kapa] κάππα
Lambda /ˈlæmdə/ (LAM duh) /ˈlæmdə/ (LAM duh) [laːbdaː] ['lamða] λάμβδα
Rho /ˈroʊ/ (ROE) /ˈroʊ/, /ˈr̥oʊ/ [ro] ῥῶ
Sigma /ˈsɪɡmə/ (SIG muh) /ˈsɪɡmə/ (SIG muh) ['siɣma] σῖγμα
Tau /ˈtaʊ/, /ˈtɔː/ /ˈtaʊ/, /ˈtɔː/ [ˈtaʊ] [taf] ταῦ
(TOW rhyming with COW, (TOW, rhyming with COW,
TAW rhyming with LAW) TAW, rhyming with LAW)
- The table, especially the all-important Classical Greek pronunciation column, is incomplete; I ran out of patience.
- For the rhyming letters Beta-Zeta-Eta-Theta, the American pronunciation (-ayta) is closer to Classical Greek and the British pronunciation (-eeta) closer to Modern Greek.
- For the rhyming letters Phi-Chi-Psi-Xi (but not Pi for some reason!) there seems to be a variant (-ee) pronunciation close to modern Greek that exists only(?) in science and mathematics.
I've made this community wiki so that someone can fix the errors or complete the table (including possibly myself if I regain the patience to finish this sometime!)