Memorizing present participle, don't understand some accents

[Banana tree]

When I memorized the paradigm for present participle I realized that there are some accents in some cases I don't understand. If we have the paradigm for παιδέω in feminine:
N παιδεύουσα παιδεύουσαι
G παιδευούσης παιδευούσων
D παιδευούσῃ παιδευούσαις
A παιδεύουσαν παιδευούσας

The cases that bothers me are dative plural and accusative plural. When I shall put an accent somewhere on παιδευουσας I know that it should be on the antiepenultima if the ultima isn't a long syllable. But α is a short vowel right? And if it weren't a short vowel then παιδεύουσαν doesn't make any sense.

I might have missed something very elemental here but I would be extremely thankful if somebody could clarify this to me, it bothers the hell out of me.

[NateD26]

The fem. part. follows the short α declension:
N/V -ᾰ | -αι (here short diphthong)
G -ης | -ῶν (always on ultima)
D -ῃ | -αις (long diphthong)
A -ᾰν | -ᾱς (always long)

So the fem. part. act. declension for παιδεύω is:
N/V παιδεύουσᾰ | παιδεύουσαι
G παιδευούσης | παιδευουσῶν
D παιδευούσῃ | παιδευούσαις
A παιδεύουσᾰν | παιδευούσᾱς

The fem. part. med./pass. declension follows the adjectival η declension after -ομεν-
and so, its accent is dependent on the way the masc. declension goes. So here
the gen. pl. will be παιδευομένων, NOT παιδευομενῶν.

[Craig_Thomas]

ε and ο are short vowels. η and ω are long.

α, ι, and υ are sometimes short and sometimes long. They are sometimes marked with macra when long (ᾱ, ῑ, ῡ), but this is typically done only in grammars and dictionaries, not in Greek texts.

The dative plural is accented on the penult because the diphthong αι can be short only when it is not followed by a consonant, such as in the nominative plural of the first declension (the same is true of οι). So the αις ending of the dative plural is long.

[NateD26]

The dative plural is accented on the penult because the diphthong αι can be short only when it is not followed by a consonant, such as in the nominative plural of the first declension (the same is true of οι).

Isn't that a tad generalizing? What about the present optative act. 3rd sg. παιδεύοι or the aorist opt. act. 3rd sg. παιδεύσαι?
I would say the best way to look at it is that, for the purpose of accentuation, the diphthong of nom. pl. in the 1st and 2nd declensions is short.

[Craig_Thomas]

The dative plural is accented on the penult because the diphthong αι can be short only when it is not followed by a consonant, such as in the nominative plural of the first declension (the same is true of οι).

Isn't that a tad generalizing? What about the present optative act. 3rd sg. παιδεύοι or the aorist opt. act. 3rd sg. παιδεύσαι?
I would say the best way to look at it is that, for the purpose of accentuation, the diphthong of nom. pl. in the 1st and 2nd declensions is short.

I said that these diphthongs can't be short when closed by a consonant, not that they can't be long when they're not closed.

That may still be a false generalisation. I've just hunted through Smyth and Goodwin and can't find support for my statement. I would appreciate being corrected.

[modus.irrealis]

I believe you're right, although I'd agree it's probably better to just list what happens when since there are so few cases (I'd also add that infinitives treat -αι as short for the accent to Nate's list).

I also agree with the "for the purpose of accentuation" caveat, since the syllables containing these diphthongs are still long metrically.