Bad battery very likely.
It is a matter of both voltage and amperage. If the car is cold - has not been run for awhile, more energy is needed to start it. In cold climates it requires even more energy to get the car started.
Then that energy must be returned to the battery. Otherwise after some number of starts (or other power uses; i.e., the lights left on) the battery will be out of energy. Dead.
Both high and low weather temperatures are hard on batteries. And especially for old, low quality, and failing/defective batteries.
You must also look into the charging system. May not be properly recharging the battery.
Plus all of the associated electrical wiring should be inspected for breaks, loose connections, corrosion, any sign of damage.
Such physical problems may or may not be visible - mechanics usually have testers of one form or another.
Starting a car by pushing or jumping is indeed becoming problematic. Much more so for newer vehicles than older vehicles. [Edit: corrected typo.]
The only way to know for sure is to read the car's manual.
[Side note: Many new vehicles cannot even be towed or pushed.. Need to be pulled up on to a flat bed truck and transported without any wheels on the road at all. Again, you need to read the manual to be sure. Tow truck people do not always know....]
And try to learn more about your car and battery - for example.
http://www.autobatteries.com/en-us/how-car-batteries-work/overview
We all just want our things to work but there is never any harm in knowing something about the "why's &how's".
Plus the extra knowledge may help prevent you from being taken advantage of by some not-so-honest shop or mechanic.