I've seen this graph mentioned on several websites showing how Kotlin (red) is eating away at Java's market share and projecting that it will overtake Java by end of 2018

Kotlin still runs on the JVM, so the Java ecosystem will remain. So if the argument is that Java has security problems (there are some, but not nearly as many as some other languages), Kotlin will inherit them unless you compile your Kotlin code to native EXEs / executables using Kotlin Native.
The Java language itself is moving very slowly since every change needs to be designed in such a way that it doesn't break backward compatibility. Carrying 20 years of baggage along wil certainly slow down the language. Kotlin on the other hand is around 5 years old and until a year ago, they were still making breaking changes in order to make sure that they don't carry bad design choices with them for the years to come.
I know many companies who will never switch, but then I also know many startups embracing Kotlin in order to speed up their development while at the same time building it on a rock-solid foundation, the JVM. Startups often move a lot faster than older companies, add Kotlin to the mix and they get to build better quality software as well as move a lot faster than their competitors using Java. At some point these startups with Kotlin will get acquired and will start to pollute the pure Java code-bases after which more developers will get exposed to it and more developers will switch.
So unless Java innovates (if you look at the mailing list, they are talking about var,/val and some other nice things which Kotlin already had in V1.0) they will lose a large chunk of developers to Kotlin; Scala has taken out a bite as well, Groovy took a bite (Groovy might die thanks to Java9 not supporting certain core things to Groovy, so those devs will probably also join Kotlin)
Then there's also Oracle being a dick sometimes and suing Google for using Java APIs in Android, this alone also left a bad taste .
Java (language) will not die anytime soon, but Kotlin will eat a large chunk of its userbase in the same way Swift consumed Objective C users.