难 nan2, difficult; hard. Kangxi radical 172 隹.
My teacher says the radical for this character is 又 but the dictionary says clearly it's 隹.
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As @50-3 has mentioned, the 难 is the simplification of the traditional character 難. Most Chinese characters are phono-semantic compounds (形声字), in which the radical hints at the meaning while the phonetic hints at the pronunciation. In the case of 難, the phonetic component is 堇 while the radical is 隹. In modern Chinese, the pronunciation of 堇 has diverged from 難, but their pronunciations in Old Chinese were presumably closer.
Why is the radical 隹, which typically refers to birds? This link gives the explanation: http://font.zenque.com/zidian/4796.html
難 originally referred to a type of bird, but because the pronunciations coincided, the character ended up being borrowed to also refer to hardship and difficulty.
Actually it depends on what you mean by "radical" which can stand for both "偏旁"(pian1pang2) and "部首"(bu4shou3) in Chinese.
They are such ambiguous concepts that even some Chinese teacher can get confused, according to Baidu Baike:
The two concepts are different in that while "部首" only includes semantic radicals (I'm not sure if there is such a term. By semantic radical I mean "形旁" in Chinese) which is rare in Chinese characters, "偏旁" includes both semantic radicals and phonetic radicals (Again, by phonetic radical I mean "声旁" in Chinese). In other words, "部首" can be seen as part of "偏旁". So it's OK to say that "the '偏旁' of '难' is '又'", if we consider "又" as a phonetic radical. But why shall we think so?
Because the semantic radicals of "难" should be "隹".
If we open our Kangxi Dictionary to study the explanation of it, we can see this:
So "难" originally means a kind of bird. Then which part of "难" stands for a "bird"? If you know the traditional form of "鸡"(chicken)—— "雞", you will find that they share the same part "隹", which exatly means "birds" with short tails. Therefore, the "部首", or "semantic radical" of "难" is "隹". And of couse you can say that "the '偏旁' of '难' is '隹'", too.
However, the development of dictionary has subdivided "部首" into "识字部首" and "检字部首". The former is actually the "部首" I explained above, while the latter is some commonly shared part of a large number of characters which helps us to look them up in dictionaries more easily. Although most of the time both are the same, they can differ from each other in some cases, as in the case of "难".
For example, "鸡","难","艰","邓", they all share the part of "又", so "又" is one of those "检字部首"s in the dictionary.
Maybe your teacher meant that you could look "难" up in the dictionay by the radical of "又".
To the best of my knowledge and after a little research:
Wikipedia defines a radical as:
a graphical component of a Chinese character under which the character is traditionally listed in a Chinese dictionary.
So saying which dictionary you're referencing would be a big help as not all are based off Kangxi radicals. But let's take a quick look at the character 难. We have two ways of breaking it down:
Both are considered radicals and both would be valid entries in a dictionary but let's take a second to look at 難. This is the traditional variant of 难. See something missing? There is no 又 present in its traditional form but 隹 still is present so let's look at the options for classifying the traditional variant:
So based off the fact you're working with simplified I wouldn't see an issue with either your dictionary's answer or your teacher's answer but the dictionary has most likely placed 难 under 隹 as that was the location for the traditional variant.
The most important reason is to keep consistency with older dictionaries. 「難」 is listed under 「隹」, so there is no reason to change that for newer dictionaries with 「难」.
The second most important reason is that 「又」 is not really a component of 「难」. 「又」 actually means something solid: It's a picture of a hand and is pronounced as yòu. Characters like 仅, 鸡, 欢, 汉, etc. don't contain 「又」, they contain an abbreviation made up of two strokes 「㇇」 and 「乀」 which is supposed to be a situational replacement for unrelated components like 堇, 奚, 雚, , etc. If all characters which contain the abbreviation were listed under radical 「又」, then the 「又」 section in the dictionary would become extremely bloated.
Characters which actually contain 「又」 usually have connections in sound and/or meaning to 「又」: 友, 受, 取, 攴/攵 (牧, 教, 敲, ...), 殳 (投, 擊, 殺, ...), etc.
This is not a "semantic radical" or "phonetic radical" reason; there's no such thing as "semantic/phonetic" radicals, and there is no rule that dictionary radicals have to be "semantic". For example, the radical for 「錦」 is 「金」, which is its phonetic component.