There are hundreds of places in every medium or large city where you can learn C++,Java,HTML,.Net,Databases etc for paying a small fee. If you want to enter the software industry you can do that anytime in your career. But how many places do you see offering analog circuit design,circuit theory,signals & systems,VLSI,HDL,digital signal processing etc ?
This is not because there is no demand for EE skills but because you can't pick up these skills later in your career.
The truth is that CS is much easier to pass and do well at the university level whereas EE is much harder.
In the professional world what really matters is your quality as an engineer not whether you are CS/EE.
If you can do a job correctly,reliably and efficiently you will never get laid off.
Whatever you choose,study it for making a living out of it & not because it secures a good job initially.