But Moses did not give any to the Kohathites, because they were to carry on their shoulders the holy things, for which they were responsible (Numbers 7:9 NIV).
The context here is the offering of six covered carts and twelve oxen by the leaders of the people at the time of the dedication of the tabernacle. Moses gives two carts to the Gershonites and four carts to the Merarites. But he did not give any to the Kohathites.
Sometimes we wonder why we are not given certain things. We wonder why God should give some of it to somebody else and gives none to us? Let us look closely at these three branches of the Levites and see what they were assigned to do to find an answer to such questions that bother us at times: The Gershonites were mainly asked to carry the curtains that covered the tabernacle. The Merarites were mainly asked to carry the frames of the tabernacle, its crossbars, posts and bases. But the Kohathites were to carry the most holy and the most sacred objects inside the tabernacle. Even that they were supposed to do only after Aaron and his sons would have covered them with cloths assigned for the purpose. The Kohathites were also warned not to touch the holy things (they had to use the poles to carry them) or go in to look at them. If they did so, they were doomed to die.
Such was the sacred responsibility that the Kohathites had. So they were not given any carts. For they were supposed to carry the most holy things on their shoulders. This was a great responsibility. So likewise, when God gives us greater responsibilities than others, He may not provide us with carts. This is so that we will discharge our duties with greater care and divine grace.