Unless you've been karyotyped and it came back XXY, your therapist is just guessing. However it is my impression that a lot more of us have feminine skeletal markers and a more female-typical body structure overall than is the case for the cis male population. This is a sign of having hypogonadism (below normal male levels of testosterone) during childhood and puberty, and is something that's often associated with intersex conditions. It's one of the lines of evidence pointing to transness being a type of intersex condition. Klinefelters is one of the things that can cause hypogonadism, but so can just about any other cause of intersex.
There's two types of hypogonadism, primary and secondary. With primary hypogonadism, the testicles are physically unable to produce enough testosterone, despite the brain telling them to do so. With secondary hypogonadism, the testicles are OK, but the brain isn't sending out enough of the signal telling them to produce testosterone. In my case, although I haven't been karyotyped, it's definitely secondary hypogonadism. That rules out Klinefelters, because Klinefelters causes primary hypogonadism.
If you've had a full set of labs done, you can actually tell from those whether you have primary or secondary hypogonadism. With primary hypogonadism, your total and free testosterone will be low, whereas your LH and FSH (the signal that tells your testicles to do their thing) will be at or near the top of the range. With secondary hypogonadism, your total and free testosterone will be low, and your LH and FSH will be towards the bottom of the range too.
The effects as far as your body's physical development is concerned are more or less the same with primary and secondary hypogonadism, however there's one important difference. With primary hypogonadism, you're likely to be infertile, but with secondary hypogonadism, there's a very good chance that you can produce viable sperm. If you are secondary and you think you might want children in the future, it's a good idea to have some of your sperm frozen before you start HRT. Once you've been on hormones for a while, it's much more difficult to get to a state where you can produce viable sperm again (and would probably mean coming off hormones for a long time).