Both should be allowed as answers, but they have different meanings.
In the sentence, "Tá sí" "tá", the verb form of "bia", is used. Roughly speaking, "Tá sí" in this context is used to express a permanent state: "She is" as in "She exists." By contrast, in answer to the question, "An í Cáit an múinteoir?", "Is Cáit the teacher?" you can respond, "Is í." meaning "Yes, she is." In the second example, the copula, and not the verb, is used to identify Cáit as the teacher.
We're talking about difference between the use of the word "bia" in its copula form and in its verb form. The copula in Irish is usually used to define and identify, but can also be used with the preposition "le" to express ownership, to give your name, and to mark emphasis by moving words toward the beginning of a sentence.
A copula (here, denoted by "is..." and one of the copula forms of "bia") is a word that connects the subject and predicate ("copulates") when there is no "normal" verb. It usually occurs in Irish only if a noun, pronoun or adjective is the predicate, as opposed to when the verb is the predicate.
This section is confusing for English speakers because copulae in the English language may be used non-copulatively. For examples, see Wikipedia's list of English Copulae. http://en.wikipedia.org/wiki/List_of_English_copulae
Be sure to check out the section entitled "The copula" in "Tips notes."
From the Wikipedia link posted above. This helped me think it through somewhat:
"In Irish and Scottish Gaelic, not only are there two copulas but the syntax is also changed when one is distinguishing between states or situations and essential characteristics. Describing the subject's state or situation typically uses the normal VSO ordering with the verb bí. The copula is is used to state essential characteristics or equivalences.
In Irish, the copula is used for things that are in a permanent state.
Is fear Liam "Liam is a man" (lit., is man Liam) Is leabhar é sin "That is a book" (lit., is book it that)
The word "is" is the copula (rhymes with the English word "hiss"). The pronoun used with the copula is different from the normal pronoun. For a masculine singular noun, "é" is used (for "he" or "it"), as opposed to the normal pronoun "sé"; for a feminine singular noun, "í" is used (for "she" or "it"), as opposed to normal pronoun "sí"; for plural nouns, "iad" is used (for "they" or "those"), as opposed to the normal pronoun "siad".
To describe non-permanent states, "to be" is used, e.g., Tá mé ag rith "I am running"."
The link for "copula" on the Wikipedia page says:
Most languages have one main copula, although some (such as Spanish, Portuguese and Thai) have more than one, and some have none. In the case of English, this is the verb to be. While the term copula is generally used to refer to such principal forms, it may also be used to refer to some other verbs with similar functions, like become, get, feel and seem in English (these may also be called "semi-copulas" or "pseudo-copulas").
So, that list is really a list of pseudo-copulas, and "to be".
bia is a noun, meaning "food".
tá is the present tense form of the verb bí.
The "state of permanence" thing seems to be brought up by people who are trying to apply things that they learned in other languages to Irish. Tá sé marbh means "he is dead", which is a pretty permanent state, whereas is mise an buaiteoir means "I'm the winner" - I can say that after a hand of cards, and it won't be true a few minutes later when I lose the next hand. The real difference is that marbh is an adjective whereas buaiteoir is a noun.
bí is a verb. Tá is the simple present tense form of the verb bí.
Irish and English both differentiate strongly between the simple present and the present continuous/present progressive. There is no equivalence between the simple present "she runs" and the present progressive "she is running". You do not use the verb "be"/bí to say "she runs", you use the verb "run"/rith - ritheann sí.
Tá sí ag rith - "She is running"
Ritheann sí - "She runs"
Tá sí déanach - "She is late"
Is reathaí í - "She is a runner"
Yes, there is more than one to say "she is".
While tá sí and is í both mean "she is", they aren't interchangeable. You can only use is í where you use the copula, you can only use tá sí where you don't use the copula.