Depends on how strong you are. but don't forget it’s a 45km climb from sea level by the time you hit Vilaflor (assuming you’re going from the south side) you will have spent well over an hour to 100 minutes in the saddle. Just to give you some idea I’m pretty fit and average 20-21mph on my 16 mile commutes I climb reasonable well (I pass most on climbs in sportives). When climbing the Tiede I was doing between 6 - 10mph (9.2mph average to be precise) I was in the saddle constantly climbing for around 90 minutes at which point I had enough and decided to lunch at Vilaflor before attacking the last 22km. I had a triple (Hired Bike) and rode 30/23 for most part 30/21 for good parts too. I jumped to the 36 ring on occasion but not very often mind you the bike was not light nor were the rations and tool kit I was carrying. The second part of the climb is the toughest not only do you have to carry water for the next 90 to 100 minutes but you also have to have enough gels and there are some nasty 12 - 14 per cent ramps. Once you plateau there is a long drag to the centre (cable car) really rough road in parts be careful.
Just before the cable car there is a very long drag not steep but it zaps your legs if you have not kept anything in reserve - I’ve read some people get illusions they are not moving on this part as the cable car does not seem to get any nearer any quicker it’s a weird illusion. Anyway and here's where you may not get through with 34/25 - In order to get to the possible highest road point the road to the cable car station needs to be attacked and its brutally steep possibly 17 per cent from memory maybe more. Not an issue on a normal day but by the time you reach it you will have been in the saddle for anything up to and over 3 hours your legs will no doubt be burning. I needed 30/32 to get up that final part although I probably could have done it with 30/28 (BTW some road bikes out there have mountain bike cassettes and I’m glad this did as well). So in answer to your question, depending on your fitness, I reckon 34/25 could climb the Teide but will it be the difference between stopping to rest the lactic acid or carrying on albeit spinning a much lower gear? If I went again I would not be comfortable unless the bike was 7KG and had 34/28. any heavier granny ring please
Heres my Garmin
record Judge if you would be better than this, if so you probably would be strong enough with 34/25 there are two splits the first to the summit (cable car station) the second coming down.
You might need a wind gilet coming down I did in August and it was 34c and don't get any illusions that its a fast flowing road its like alp due'z too many switch backs to get a decent descent without constantly breaking and where you do get a bit of straight road its rough as, in parts and not very comfortable at 45mph+
In summary its not that hard a climb steepness (in climbing terms) it just goes on forever and ever. For the majority you might well be above the clouds than below them that's how high it is
Good luck I only wish I was there to keep you company
