@JanMurphy has provided some useful suggestions for trying to locate Matthew in this census. However, the unfortunate truth is that the 1861 census has been well-indexed on many sites now, so the pessimist in me says that as you and others have done an extensive search for him it is unlikely you will find him anywhere on this census. This answer looks at some of the common reasons why you may be unable to find him.
The key to remember with all these possible explanations is that the census is a snapshot in time. It is where everyone was one night in 1861. That may be different to where they were the day before and the day after.
Simple mistake or omission
This is, in my opinion, the most likely explanation for Matthew's absence on the census.
It is possible Matthew was staying with his parents the night of the census. This census was carried out in the same way all the other English censuses were carried out. An enumerator would deliver a form (schedule) to the householder a few days before census day. The householder would fill in this form at some point in that week, and then shortly after census day the enumerator would be back to collect the forms. The enumerator would then transfer all the information on the schedule over to the enumerator's book, which is what we have access to today.
It is very possible that in transferring the information over from the schedule to the enumerator book, he skipped a line. I have transcribed many records before, and it is very easy to mistakenly skip a line.
Another explanation is that Matthew's father omitted him from the schedule for some reason. As previously mentioned, the forms were delivered a few days before census day, so if they were filled out a day or two in advance, and Matthew changed plans as to where he was staying on census night, he might not end up on any form.
Similarly, if Matthew was just spending one night (census night) in another house, the householder there may have incorrectly assumed he was enumerated with his parents and thus not included him.
Missing piece or folio
Unfortunately, there are some pieces, or parts of pieces, that have been lost for every census - including the 1861. A list of 1861 census pieces known to be missing in part or entirety is given on FindMyPast.
I cannot see any Cornwall pieces that are specifically noted on this list, but it is possible Matthew could have been in another county on census night for which the record has gone missing.
This census has been transcribed on several sites, and it is unlikely they would all make the same transcription error. However, it is possible that the page is damaged or very difficult to read, which means he may not appear correctly on any index. Often creative searching of other fields (e.g. birthplace) can make it possible to identify an individual.
Recorded as "Unknown" or "Stranger"
It is not uncommon to come across entries, particularly in lodging houses, where an individual is recorded as "unknown", "stranger", or the like. This could occur when the individual who was staying the night there left early the next morning before their details could be noted for census purposes. If Matthew was one of these individuals, it would be next to impossible to identify him.
In an institution
Perhaps a less likely explanation for Matthew's absence - but one to consider - is that he was in an institution on the night of the census. He could have been in a hospital for a night, or in a prison. Often these institutions recorded their patients or inmates by initials only (e.g. M. N.), so even by an extensive search you could miss them. You might use newspapers or institutional records to corroborate this theory.
In the army or abroad
This is very unlikely in your case given that Matthew was only 14-15, but included for completeness. Those in the army or abroad would not be found on the census. The 1861 Worldwide Army Index on FindMyPast is a good substitute for finding soldiers abroad at the time of the census.
I think it is unlikely that the reason you cannot find Matthew was because he was undertaking his apprenticeship elsewhere. It is certainly possible, but having spent quite a considerable amount of time searching for him on several websites, I think there would also be another reason we cannot find him - either an omission or major transcription error.
I hope that you are able to find Matthew on this census - so am not suggesting you give up looking. However, I hope I have emphasized some of the more common reasons why someone simply might never be able to the be found on a UK census.