One disadvantage of a letter of the week approach to teaching the alphabet is the pace. When you are only teaching one letter each week, it takes 26 weeks to get through the entire alphabet. This is over 6 months of instructional time. Any children who come to school already able to identify any of their letters will find this much review to be uninteresting and unnecessary. Instead of teaching one letter per week many teachers find it more effective to teach one letter per day or a group of letters each week.
With a letter of the week approach the letters are typically taken out of the context of real reading. Children learn the letters in isolation but do not learn about blending them into sounds to make words. Learning letters in isolation does not teach children how to apply this knowledge to what they are reading. A letter of the week approach also often has children learning to copy and write particular letters of the alphabet but again, they do it without any context.
Some letters are more difficult to learn and distinguish than other letters. For example, lower-case b, d, p and q all look similar but are widely spaced in the alphabet. When it comes to learning letter sounds consonants that only have one sound are much easier to learn than vowels that can make several different sounds. In a letter of the week approach all of these letters receive equal amounts of instructional time although some letters are more difficult to master.
A letter of the week approach does not account for the fact that some of the most commonly used letters of the alphabet appear at the end. These include the letters r, s and t which would not be taught until after January with a letter of the week approach. In addition, a child whose name started with the letter t or w would have to wait until very late in the year to learn about "his" letter.