Perhaps to you that seems like a bold statement, something radical and unacceptable. But allow me to explain...
There is no universal definition of terrorism, but there are some rules as to what is widely classed as such. Terrorism is an act done because the party responsible for the terrorising has a political agenda. These killings do not seem senseless to them because they see themselves trying to achieve a legitimate, political goal. To them, their needs are being ignored by the world - and so they see fit to bring attention to themselves in the only way that is left.
As citizens of the western world, we seem to have a very blinkered vision over what constitutes terrorism and in turn a terrorist. By the way we now define terrorism, those who acted out as radical feminists during the suffragette movements in the late 19th century and the early 20th century were terrorists. They broke laws, incited fear and created an illegal social movement. And yet now, as a society where greater gender equality now exists and is almost universally supported, we look up to those women.
The difference here is that we support what they were fighting for. We support their ideas and their goals and so the means they used seem brave and not radical to us now.
Nelson Mandela was also a terrorist. Yes, he became president and is seen globally as a symbol of peace, but before that, when he was fighting to be heard, he was a terrorist. He served 27 years in prison after leading a sabotage campaign against his government. Despite most of the world supporting him in his aims for ending the apartheid and his mission of equality, his means were unarguably radical. Yet to most of the world he is now seen as a positive role model for his work towards such a noble cause.
The term terrorist sympathiser is misused to mean supporter. People are capable of feeling sympathetic towards someone who's plight is so desperate that they resort to measure such as violence whilst still feeling disgusted by the acts they carry out. In this context this is a problem, and not something to support. However - terrorists incite terror because they are trying to reach a political aim and are not being heard. In order to fix the problem at it's root, it's important to have sympathy for the cause these people are fighting for - and it is perfectly possible and also essential that we sympathy for their cause, without feeling sympathetic towards their methods.
In my personal opinion, the best way to combat terrorism is to conduct peace and negotiation talks with the leaders of groups who have taken it upon themselves to use terrorism to reach their aims. Trying to eradicate groups like Islamic State by increasing national security sounds like a good idea in principle. But this fixes the problem not the cause, and of course it can never be fully successful. Fixing the problem at it's root is not only more successful, but it also means that countries don't have to spend money on military and security, whilst all the time fearing imminent attack. Political talks to solve problems in the originating countries is more than likely the only solution to an ongoing terror problem.
To conclude, while it is never correct to show support for the actions of terrorists, listening to and searching for the causes behind their immoral acts ensures that not only are you more educated on the topics, but you better understand the causal factors behind the evil faces on the news. What they are doing may not seem bad to their people, who believe in what they are fighting for.