There are different nusachot that count sfirah as "ba'omer" or "la'omer." But shouldn't we count days m'omer? The omer was brought on the 16th and that's what we are counting from. Leviticus 23:15 says: וּסְפַרְתֶּם לָכֶם, מִמָּחֳרַת הַשַּׁבָּת, מִיּוֹם הֲבִיאֲכֶם, אֶת-עֹמֶר הַתְּנוּפָה: שֶׁבַע שַׁבָּתוֹת, תְּמִימֹת תִּהְיֶינָה. So why are we counting days "in" the omer or "of" the omer instead of counting "from" the omer?
Perhaps the flip side of the question is what do "baomer" and "laomer" mean? The omer is a sheaf of grain, what does it mean to have days "in" or "of" the sheaf? The Torah does not call the days themselves "the Omer."