how could it categorically be said that there is not a seasonal factor causing the peaks and troughs?
Read what Roxxii said:
For a time series to be seasonal, there needs to be a regular time interval between each peak.
Yes, you can ASSUME that there is a regular cycle of every 6 months, peaking every May and Nov (month 5 and 11)
But we are only given one year of data, and there is only ONE interval between the peaks.
There is no indication how many months there will be between the peak at month 11 and the next peak (if there is a peak at all)
Thus you cannot come to the conclusion that it is seasonal with the information given to us.
If there were AT LEAST 3 peaks, so 2 intervals in between...and the intervals had the same number of months, then it would be reasonable to assume the trend is seasonal.