why is the phosphate buffer made up by using the Henderson-Hassalbalch equation not the expected pH?
The Henderson-Hasselbalch equation is used mostly to calculate pH of solutions created mixing known amounts of acids and conjugate bases (or neutralizing part of acid with a strong base). For example, what is the pH of a solution prepared mixing reagents so that it contains 0.1 M of acetic acid and 0.05 M NaOH? Half of the acid is neutralized, so concentrations of acid and conjugate base are identical, thus the quotient under logarithm is 1, the logarithm is 0 and pH=pKa.
This approach - while perfectly justifiable in many cases - is dangerous, as it creates false conviction that the equation can be used this way always. That's not true.
The Henderson-Hasselbalch equation is valid when it contains equilibrium concentrations of an acid and a conjugate base. In the case of solutions containing not-so-weak acids (or not-so-weak bases) equilibrium concentrations can be far from those predicted by the neutralization stoichiometry.
If you are looking for a way to calculate buffer composition, you can reverse the equation. Using known pH and known pKa you can calculate the ratio of concentrations of the acid and conjugate base, necessary to prepare the buffer. Further calculations depend on the way you want to prepare the buffer. You will find several examples of buffer composition calculations at buffer lectures.
Note: if you need program that will help in buffer calculation, you can try our Buffer Maker - the ultimate buffer calculator.