The reason is that the NetCDF interface you are using is very low-level, and all you have done is read out the variable without any of its dimension information. The orientation of the grid is really arbitrary, and the coordinate information needs to be understood in a particular context.
library(raster) ## requires ncdf package for this file
d <- raster("LPRM-AMSR_E_L3_D_SOILM3_V002-20120520T185959Z_20040114.nc", varname = "soil_moisture_c")
(I used a different file to yours, but it should work the same).
It turns out that even raster does not get this right without work, but it does make it easy to rectify:
d <- flip(t(d), direction = "x")
That transposed the data and flipped around "x" (longitude), keeping the georeferencing from the original context.
Plot it up with a map from maptools to check:
plot(d)
library(maptools)
data(wrld_simpl)
plot(wrld_simpl, add = TRUE)
There are many other ways to achieve this by reading the dimension information from the file, but this is at least a shortcut to do most of the hard work for you.
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