How to counter Irelia
Let us take a look on how to beat Irelia. We will look at champions who are strong against Irelia and who are weak against Irelia. Use win rate, gold difference and creep score difference at minute 10 to find the best 
Top champion who counters Irelia. You can already win in champion select with the right counters for Irelia. If you want to know how to counter Irelia then you need to take into account the best picks vs Irelia and the worst picks vs Irelia. This Irelia counter data is based on matches played by Pros on patch 13.24 and previous ones. It is important to see whether Pros counter picked Irelia or whether they played as Irelia.
Champions used by Pros to counter pick Irelia
Looking at the matches from Pros (see table Pros counter picked Irelia) we can see that they picked 
Rumble most often to counter pick Irelia. The matchup Rumble vs Irelia occured 26 times. Irelia has 15 wins and 11 losses in this matchup. Learn how to counter pick Rumble to get another perspective on the data.
Lane outcome for Irelia
When looking at Irelia counters you will notice that win rates alone are not conclusional. Therefore we provide an overview (see table Lane Outcome) where you can see the lane outcome of Pros who played Irelia. The lane outcome of Irelia consists of three outcomes: Win, Loss or Draw. Let's take a look of Irelia lane and match outcome for specific matchups. Considering the lane outcome and the match outcome of a specific matchup, might enable you to find the right counter for Irelia.
Conclusion
Analyze the available data and learn how to beat Irelia. To master Irelia take also a look on Irelia builds and runes for Irelia. Good luck, Summoner!