I can provide some general information about the rarity of INTP and INFJ personality types, and why they might be considered as such.
INTP (Introverted, Intuitive, Thinking, Perceiving): INTPs are often considered one of the rarest personality types, making up a relatively small percentage of the population. Their preference for introversion and intuition, combined with a thinking and perceiving orientation, makes them less common compared to other personality types. INTPs are known for their analytical and logical thinking, their deep intellectual curiosity, and their unique approach to problem-solving.
INFJ (Introverted, Intuitive, Feeling, Judging): INFJs are also considered one of the rarer personality types, although estimates of their prevalence may vary depending on the source. Like INTPs, INFJs possess a combination of introversion and intuition, but they differ in their preference for feeling and judging. INFJs are often seen as empathetic, compassionate, and insightful individuals, with a strong focus on understanding others' emotions and needs.
As for which one is rarer between INTP and INFJ males specifically, it's challenging to provide precise data on this aspect. Personality type distribution can vary across different cultures, populations, and age groups, so it's essential to refer to large-scale, up-to-date studies or surveys to obtain more accurate information. However, both INTP and INFJ personalities are generally considered relatively rare compared to other types.
Keep in mind that discussing rarity shouldn't be interpreted as one type being more valuable or better than another. Every personality type has its strengths and weaknesses, and diversity in personality enriches the human experience.