Concept:
Articles are words used before nouns to indicate whether the noun is specific or non-specific. The choice between “a” and “an” depends upon the sound with which the following word begins, not merely on the first letter of the word.
Step 1: Identify the noun before which the article is to be used.
The noun used in the sentence is “honour”.
\[
\text{He is \_\_\_\_\_\_ honour to his profession.}
\]
Therefore, we need to determine the correct article before the word “honour”.
Step 2: Examine the pronunciation of the word “honour”.
Although the word “honour” begins with the letter “h”, the letter “h” is silent in pronunciation.
Thus,
\[
\text{honour} \rightarrow \text{onour}
\]
Since the word begins with a vowel sound, it requires the article “an”.
Step 3: Apply the rule for the use of indefinite articles.
The article “an” is used before words beginning with a vowel sound.
Examples:
\[
\text{an hour, an honest man, an heir, an honour}
\]
Hence the correct sentence becomes:
\[
\text{He is an honour to his profession.}
\]
Therefore,
\[
\boxed{\text{an}}
\]