ODBC_COM = New OdbcCommand("UPDATE President SET '" & President_UPDATE_field.Text & "'='" & President_UPDATE_text.Text + "'", ODBC_CON)
        ODBC_COM.ExecuteNonQuery()

i dont know why im having error like this, what i know is my syntax for UPDATE command is correct and im using correct number of single quotes and double quotes

Close, but no cigar.
Try it like this instead.
Notice that I removed some single-quotes and changed the plus-sign (+) into an ampersand (&).

ODBC_COM = New OdbcCommand("UPDATE President SET " & President_UPDATE_field.Text & " = '" & President_UPDATE_text.Text & "'", ODBC_CON)
ODBC_COM.ExecuteNonQuery()

Also. If you put it all inside a Try...Catch statement, you can put a MessageBox.Show(ex.ToString) inside the Catch to see what's going on if an error occurs.