Why does the pronunciation of 'ABA' ( אבא ) is straightforward, while the pronunciation of 'IMA' ( אמא ) is not ?
Shouldn't it be pronunciated 'AMA' instead of 'IMA' ?
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(I'm assuming your question relates to how the writing relates to the pronunciation, rather than how the words came about historically. Correct me if I'm wrong. I'm also approaching this from an Aramaic perspective rather than a Modern Hebrew one; both of these words are Aramaic in origin, and the spelling given in the question is the Aramaic one.)
The Aramaic writing system didn't generally indicate vowels the way the Greek, Latin, and Cyrillic alphabets do. Certain letters, such as aleph, can either indicate a consonant or a long vowel. And short vowels are just unwritten. Compare the modern Arabic alphabet.
There is, however, a convention called "pointed writing" (as well as probably fancier names, but that's the one I learned) where diacritical marks are placed on letters to indicate how they're actually pronounced. That makes it much clearer.
The first word you mention is written in "pointed writing" as אַבָּא ʾabbā. The second word is אִמָּא ʾimmā. In both of these, the first aleph doesn't indicate a vowel a, but rather a consonant: the glottal stop. The short vowel following that glottal stop doesn't get its own letter.
NB: It doesn't get its own letter in Aramaic, at least. In Modern Hebrew, the use of actual letters for vowels has become more widespread, whether the vowels are long or short. As har-wradim points out, the second word is thus prescriptively spelled אימא, with the i explicitly marked. Yiddish has taken this trend to its obvious conclusion, using letters for all vowels.
(Historically, the different vowels in these roots seem to go back to Proto-Semitic.)
The story behind אמא and אבא is slightly more complicated than explained in Draconis' answer.
Jewish Aramaic (the two words in question are of Aramaic origin - see below) and all stages of Hebrew were/are written in square script which originally did not have means to denote vowel sounds.
The two mutually non-exclusive strategies used to assist the reader are: 1) the addition of special vocalization diacritic symbols and 2) introduction of matres lectionis, i.e. consonant letters denoting vowels. Vocalization marks came very late and are/were rather inconvenient in day-to-day writing. The general trend in the development of Hebrew writing has thus been the more extensive usage of matres lectionis.
The four matres lectionis in use in Hebrew and Aramaic are:
There was indeed a tendency for the matres lectionis to be written in long syllables, but this is not evident in Modern Hebrew writing.
Now to the words in question. Both אמא and אבא are Aramaic words and in such shape they entered Mishnaic Hebrew. The motivation for the lack of י in אמא is likely twofold: first, the corresponding syllable was closed by the geminated m (it must be said though that in Aramaic orthography closed-syllable vowels could be denoted with matres lectionis as well) and second, the word was easily recognized without י. In Modern Hebrew, nevertheless, the spelling אימא is prescribed, although this prescription is to a large extent ignored.
Interestingly, Hebrew preserved also the original Hebrew words for father and mother:
Proto-Semitic *ʔimm > ... > Tiberian Hebrew אֵם /ʔem/ [ʔe:m] (inflected /ʔimm-/) ~ Modern /em/
Proto-Semitic *ʔimm > ... > Judeo-Aramaic אִמָּא */ʔimma:/ > ... > Modern /ima/
Proto-Semitic *ʔab > ... > Tiberian Hebrew אָב /ʔɔ̄v/ [ʔɔ:v] ~ Modern /av/
Proto-Semitic *ʔab > ... > Judeo-Aramaic אַבָּא */ʔabba:/ > ... > Modern /aba/