Answer: The awful truth is that even in the realm of music there will be some issues on which authorities differ. Your example falls right in the middle of two acceptable views.

Beaming and tying should be used to make the reader's task easier by clarifying the structure of a measure. Personally I have a visceral dislike for the sort of beaming encountered frequently in certain composers in which the natural metric group is obscured by a beam that crosses a division, like the following:

P. Tchaikovsky, 1812 Overture, viola:

The composer or - who knows - his editor - is trying to show the musical pairing of those notes via the beaming, but it's an invitation to misreading by nearsighted orchestra members not at the peak of their attention spans. The pairs give the impression that they begin on downbeats. I'd rather it were written this way:

Your example is more ambiguous. Our readers will see that the teacher's recommendation produces a clear visual representation of the metric structure in that 4/4 measure, which naturally divides in the middle. So that teacher has a good point to make; it's a wise principle not to cross a metric division with a long note unless it begins at the start of the measure.

However, there are some syncopated patterns that are so familiar that one can get away with breaking that metric structure; and the version recommended by the theory book meets that description: it's still easy to read. For that reason our Songworks software, if you ask it to automatically do this for you, will allow a minim to cross the center line so long as the minim begins on a beat.

Similarly, Mozart felt pretty comfortable writing syncopated quarter notes (crochets, to you in the mother country) this way in his Symphony No. 25:

That's such a familiar device that it's probably actually easier to read than strict metric tying like this:

To get back to your example, if you're not sick of this yet, I'd say that the teacher's rule would absolutely have to be followed if that minim (half note to us Americans) did not begin on a beat, or perhaps even if it were a dotted note starting on a beat other than beat one. An offbeat note crossing the metric divide is very hard to read; a note beginning on a beat is easier, even if dotted. So the first of the following would not be acceptable. The second is OK and will be encountered, but one could argue that the third version is better still because it shows the metric division of the measure:

Gardner Read, author of what is probably the standard work on notation (Music Notation: A Manual of Modern Practice) doesn't quite admire using a dotted note as above, but even so he doesn't make a strict rule but says that it "may be better" to get rid of a dotted note that crosses the metric division, substituting a tie. Why not make things clearer, after all? Here's the example he uses:

So, I'd want to modify that rule you mention, to "avoid ties when possible." "Possible" covers a lot of territory; my "bad" example above is still "possible" and so are the two examples that show dotted notes crossing the center of the measure. It would be better to say, "avoid ties if they do not help to clarify the rhythm." For resolving the dispute between the Music Theory Book and your daughter's teacher, I must say that both have a legitimate case. But if your daughter were ever marked "wrong" for tying as her teacher has suggested, we could take that to the Supreme Court (here in America, that is) and we would certainly triumph. She would not be wrong, merely more fastidious than some think necessary.