Quite simply, Mace Windu - and many other Jedi Masters - did NOT trust Anakin Skywalker. There had always been a darkness about him, ever since he was first introduced as a child. Beyond that, he often proved to be reckless, headstrong, and ambitious - all attributes the Jedi attempted to avoid. In fact, they were typically the attributes of the Sith. This was first hinted at when young Anakin was being evaluated by the Jedi Council:
YODA: Afraid are you?
ANAKIN: No, sir.
YODA: See through you, we can.
MACE WINDU: Be mindful of your feelings...
KI-ADI: Your thoughts dwell on your mother.
ANAKIN: I miss her.
YODA: Afraid to lose her... I think, hmm?
ANAKIN: (a little angry) What's that got to do with anything?
YODA: Everything. Fear is the path to the dark side... fear leads to
anger... anger leads to hate.. hate leads to suffering... I sense much
fear in you.
Yoda mentions it again when informing Kenobi of the Council's decision:
YODA: Confer on you, the level of Jedi Knight the Council does. But
agree on you taking this boy as your Padawan learner, I do not.
OBI-WAN: Qui-Gon believed in him.
YODA: The Chosen One the boy may be; nevertheless, grave danger I fear
in his training.
OBI-WAN: Master Yoda, I gave Qui-Gon my word. I will train Anakin.
Without the approval of the Council if I must.
Both Mace and Yoda had often discussed both the potential and danger of Anakin Skywalker, yet both trusted Obi-Wan Kenobi implicitly. It was their hope that Kenobi's teachings would "smooth out" the rough spots in Anakin and eventually help him become true to the Jedi Way.
Much of this disagreement about Anakin takes place off-screen, so this statement serves two purposes - A) it sums up the mistrust of Anakin in a single sentence, but also B) shows that Anakin can still be redeemed at this point.
MACE WINDU: Then our worst fears have been realized. We must move
quickly if the Jedi Order is to survive.
ANAKIN: Master, the Chancellor is very powerful. You will need my help
if you are going to arrest him.
MACE WINDU: For your own good, stay out of this affair. I sense a
great deal of confusion in you, young Skywalker. There is much fear
that clouds your judgment.
ANAKIN: I must go, Master.
MACE WINDU: No. If what you told me is true, you will have gained my
trust, but for now remain here.
The title of Jedi Master is given to a Jedi Knight to show that they have an advanced understanding of the Jedi Way & The Force. In essence, a Jedi Master should embody the traits and ideals upheld by the Jedi Order. In the minds of many Masters, this is something that Anakin hadn't even come close to yet. To achieve the title, he would not only need to change his attitude considerably, but also pass the trials like any other Jedi Knight.