when multiple pattern rules match a target

The GNU make manual says

It is possible that more than one pattern rule will meet these criteria. In that case, make will choose the rule with the shortest stem (that is, the pattern that matches most specifically).

So it surprised me that:

$ touch make_specific.cpp

$ cat Makefile.general_first
%.o: %.cpp
@echo using general rule
$(CXX) -c $< -o $@

%_specific.o: %_specific.cpp
@echo using specific rule
$(CXX) -c $< -o $@

$ make -B -f Makefile.general_first make_specific.o
using general rule
g++44 -c make_specific.cpp -o make_specific.o

Multiple pattern rules match the target, and since the stem for the %_specific.o : %_specific.cpp rule ('make' in this case) is shorter than the stem for the %.o : %.cpp rule, I expected the specific rule to be selected, but it's not.

What am I missing?

You are probably using a make version lower than 3.82.

In version 3.81 and lower, the selection criterion was different; make would choose the first rule that matched the pattern. The documentation you are referring to is for version 3.82. That version does choose the rule with the most specific stem, which is according to your expectations.

From the file NEWS in the make source tree:

Version 3.82
...
* WARNING: Backward-incompatibility!
  The pattern-specific variables and pattern rules are now applied in the
  shortest stem first order instead of the definition order (variables
  and rules with the same stem length are still applied in the definition
  order). This produces the usually-desired behavior where more specific
  patterns are preferred. To detect this feature search for 'shortest-stem'
  in the .FEATURES special variable.