i cant believe that this guy wont listen. here.
look at the f2l algorithms. if you dont, look at badmephistos f2l tutorial video on youtube. the f2l algorithms are all the cases you will come across. the difference between intuitive f2l and algorithmic f2l is that with intuitive, you set up each case into one of 3 basic cases, RUR', L'UL, or hiding and edge and positioning the corner above it to make a pair and then inserting the pair. the biggest difference i find between intuitive and algorithmic is that intuitive f2l knowledge will not allow you to solve bad cases efficiently. taking a look at the algorithmic f2l does not mean that the cubers here are telling you to memorize algs. this means to simply go over each case with the algorithm there so you can understand what it looks like to make the pair and insert it. what do we mean by sticker on the right, sticker on the left, on the top?
f2l takes a lot of time because of 2 things. in the beginners method you are looking for only 1 piece at a time, once you see that piece, you work on that piece. 2nd thing is that once you find your corner and corresponding edge, how do you pair them? how do you insert them? . . . these 2 things are what are slowing you down. looking for 2 pieces when you were only accustomed to looking for 1, and then the problem of how to pair them. . . looking for 2 corresponding pieces will come with time, and lookahead for the next pair while you are solving another pair, in much much more time and practice. with how to insert them and pair them, however, the speedsolving wiki and badmephisto's or even westons f2l tutorials are the way that MANY people learned intuitive f2l.
you will know when you have to dip into the alg database for a bad intuitive f2l case. however, i know you will be shocked when the many of the algs in the database will match up with the way you solve them intuitively.
there are many many threads regarding this issue of having problems with f2l. please use the search function within the forum to look for a solution or ask in the one question answer thread.
wait until you start learning PLL and you screw up an alg and have to start all over with f2l again during your solve. haahahha. every step of learning CFOP can be a pain if you dont have patience.