Why in a ברכה for a commandment (for example, hand washing, Tefillin etc.) do we switch between 'You' ברוך אתה and 'His' במצותיו ?
Why don't we say במצותיך ?
This is addressed by Rashba, Responsa V, 52.
After stating that there is a kabbalistic reason for this form of blessings, he offers a revealed explanation as well:
קבעו הנוסח בנגלה ונסתר. ברוך אתה, כמדבר עם מי שהוא נמצא מפורסם, עם שהוא מדבר עמו פנים אל פנים. וכדי שלא תשבש המחשבה שהוא ית' נמצא כמציאות שאר הנמצאים, ושיש יחס בין מציאותו למציאותם, קבעו: אשר קדשנו; לקבוע בנפשותינו שאע"פ שהוא מפורסם, מהות מציאותו נעלם ונסתר שאי אפשר לדבר בו, רק בנסתר, ברוך הוא.
They fixed the text in the second and third person. ‘Blessed are you’, as if he is speaking to someone present and known, someone with whom he speaks face to face. But so that one does not make the mistake of thinking that He (the Blessed One) exists like other things exist, and that there is a relationship between His existence and their existence, they fixed ‘Who has commanded us’, to fix in our minds that although He is known, the essence of His existence is lofty and hidden, and it is impossible to speak of it, apart from in the third person, blessed is He.
Another way of explaining it might be that when we daven(pray), we should develop the feeling that we are close to and speaking straight to Hashem (G-d) and can tell/ask Him anything, but at the same time, we must remember that He is greater than we'll ever know and He is not one of us, so we speak to Him in a respectful third person.